__Quantitative__

__Aptitude__

__BOATS AND STREAMS__
1. A man's speed with the current is 15 km/hr. and the speed of the current is 2.5 km/hr. The man's speed against the current is:

A. 8.5 km/hr. B. 9 km/hr. C. 10 km/hr. D. 12.5 km/hr.

Ans : Man’s speed-currentspeed =(15-2.5)-2.5=10 ie C

2. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

A. 2 : 1 B. 3 : 2 C. 8 : 3 D. Cannot be determined

Ans: The ratio of running time, the ratio of speed of upstream and dowstream ie 528:240 =11:5. The ratio between the speed of boat and speed of current =11+5/2:11-5/2=8:3

3. A motorboat, whose speed in 15 km/hr.in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr.) is:

A. 4 B. 5 C. 6 D. 10

Ans: Let speed of the stream be x then 30/15+x +30/15-x=9/2 ie 9x

^{2}=2025-1800 ie x^{2}=25 x =5
4. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

A. 4 km/hr. B. 6 km/hr. C. 8 km/hr. D. Data inadequate

Ans : Downstream speed=16/2=8 Upstream speed =16/4=4 then boat speed=8+4/2=6 stream speed =8-4/2=2

5. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance traveled downstream in 12 minutes is:

A. 1.2 km B. 1.8 km C. 2.4 km D. 3.6 km

Ans : The speed of downstream =15+3 =18 covered in 12mts ie 18/5=3.6km

6. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

A. 2 mph B. 2.5 mph C. 3 mph D. 4 mph

Ans : The ratio of time taken 3:2 then ratio of speed is 10-x:10+x =3:2 ie 30-3x=20+2x ie x=2

7. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

A. 2.4 km B. 2.5 km C. 3 km D. 3.6 km

Ans : Total time taken =x/5+1+x/5-1=1 ie 10x=24 ie x=24km

8. A boat covers a certain distance downstream in 1 hour, while it comes back in 1.30 hour. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

A. 12 kmph B. 13 kmph C. 14 kmph D. 15 kmph

Ans :Let x is the speed of boat then x+3=(x-3)3/2=2x+6=3x-9 ie x=15

9. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

A. 40 minutes B. 1 hour C. 1 hr 15 min D. 1 hr 30 min

Ans : the speed of boatman along current is 1*60/10=6km and against 2km then the boat speed is 6+2/2=4 for 5km in still water it requires 5/4=1hr 15min

10. A man can row three-quarters of a kilometer against the stream in 11 minutes and down the stream in 7 minutes. The speed (in km/hr.) of the man in still water is:

A. 2 B. 3 C. 4 D. 5

Ans : The ratio of time taken 11:7 the ratio of speed against and with also 11:7 then the speed of man is 9

11. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

A. 16 hours B. 18 hours C. 20 hours D. 24 hours

Ans: The total time taken =105/10.5+105/7.5=24

12.A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

A. 2 : 1 B. 3 : 1 C. 3 : 2 D. 4 : 3

Ans: The ratio of speed of against and favour the stream is 2:1 then the speed of boat is 3/2 and stream is ½ ie 3:1 ratio

13. A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

A. 1 km/hr. B. 1.5 km/hr. C. 2 km/hr. D. 2.5 km/hr.

Ans : 48/4/x+48/3/x=14 ie x=1/2 with stream 8 and against 6 the rate of stream is ½(8-6)=1

14. A swimmer covers a distance of 28 km against the current and 40 km in the directions of the current. If in each case he takes 4 hours, then the speed of the current is:

A. 2.5 B. 3.5 C. 1.5 D. None

Ans :The speed of boat against current =28/4=7 with current 40/4=10

Then the speed of boat =(10+7)/2=8.5 then current speed =8.5-7=1.5

15. A man can row 7.5 Kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.

A. 2 B. 3 C. 2.5 D. 4

Ans : (7.5+x) =2(7.5-x) ie 3x =7.5 then x =2.5

16. A boat takes 19 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?

A. 160 B. 180 C. 200 D. 220

Ans : Let x be the distance X/18+X/10*2 =19 ie 38x=19*360=180

17. The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?

A. 22 B. 23 C. 25 D. 24

Ans : 10/(x +2)+10/(x-2) =55/60 ie 11/12 11x

^{2}-240x-44 ie x=22
Source : http://sapost.blogspot.in/

__LOGARITHM__
18. Which of the following statements is not correct?

A.log10 10 = 1 B.log (2 + 3) =log (2 x 3) C.log10 1 = 0 D.log (1 + 2 + 3) = log 1 + log 2 + log 3

Ans : B log(2+3)=log 5 log (2x3)=log 6

19. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

A.2.870 B.2.967 C 3.876 D.3.912

Ans : log 5 512 = log 5 (2

^{9}) =log (2^{9})/log 10/2 =9 log2 /log10-log 2=9*3010/1-0.3010=3.867
20. If log 27 = 1.431, then the value of log 9 is:

A. A.0.934 B. B.0.945 C. C.0.954 D. D.0.958

Ans : log 3

^{3}=1.431 ie 3log3 =1.431 ie log3 =0.0477 log9 =2log3 ie 0.0477x2=0.0954
21. If log a/b +log b/a = log (a + b), then:

A. a + b = 1 B. a - b = 1 C. a = b D. a2 - b2 = 1

Ans : log (a+b) =log(a/b*b/a) =log 1 =1

22. If log10 7 = a, then log10 (1/70) is equal to:

A. -(1 + a) B. (1 + a)-1 C. a/10 D. 1/10a

Ans : log

_{10}(1/ 70) = log_{10}1-(log_{10}7+log_{10}10) = –(a +1)
23.If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

A. 1 B. 3 C. 5 D. 10

Ans : log10 (5(5x + 1) =log10(x+5)+log10 10 ie log25x+5=log10 (10(x+5))=10x+50 then 15x =45 ie x=3

24.The value of log3(1/60) + log4(1/60) + log5(1/60) is:

A. 0 B. 1 C. 5 D. 6

Ans : log60 3+log60 4+log60 5 ie log60 (3*4*5) =log60 60 =1

25. If logx y = 100 and log2 x = 10, then the value of y is:

A. 210 B. 2100 C. 21000 D. 210000

Ans : log 2 x =10 => x= 2

^{10 }log x y =100 y=x^{100 }ie y =2^{1000}
26. If logx 9/16=-1/2, then x is equal to:

A. -3/4 B. 3/4 C. 81/256 D. 256/81

Ans : logx 9/16 =x-1/2=9/16=√x =16/9=x=256/81

27. If log10000 x = ¼ then x equal to

A. 1/10 B. 1/100 C. 1/1000 D. 1/10000

Ans : log 10

^{4 }x =1/4 ie 4log 10 x =1/4
28. If log4

*x*+ log2*x*= 6, then*x*is equal to:
A. 2 B. 4 C. 8 D. 16

Ans : 2log2 x +log2 x =6 ie 3log2 x =6 x=2

29. If log5 (

*x*2 +*x*) - log5 (*x*+ 1) = 2, then the value of*x*is:
A. 5 B. 10 C.25 D.32

Ans: log5(x2+x)/x+1=2 ie x2+x/x+1=5

^{2 }ie x(x+1)/x+1 =x=25
Source : http://sapost.blogspot.in/

__PARTNERSHIP__
30. A and B invest in a business in the ratio 3: 2. If 5% of the total profit goes to charity and A's share is Rs.855 the total profit is

A. 1425 B.1500 C. 1537.50 D.1576

Ans: 95 % of 3/5 ie 57 % is Rs 855 then 100% = 855/57*100=1500

31. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs.6500 for 6 months, B, Rs.8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs.7400. Calculate the share of B in the profit.

A. Rs.1900 B. Rs.2660 C. Rs.2800 D. Rs.2840

Ans : Profit to be shared 7400-5%of 7400=7400-370=4030 the ratio of investment 6500*6:8400*5:10000*3 =39:42:30 then B Profit = 42/111*4030 = Rs2660

32. A, B and C enter into a partnership in the ratio 7/2:4/3:6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs.21,600, then B's share in the profit is:

A. Rs.2100 B. Rs.2400 C. Rs.3600 D. Rs.4000

Ans : Ratio of investment =(7/2)x4+(7/2+7/4)x8 : (4/3)x12 :(6/5)x12 = 35:10:9 ten B profit=10/54*21600=4000

33. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

A. 5 : 7 : 8 B. 20 : 49 : 64 C. 38 : 28 : 21 D. None of these

Ans : 14x:8y:7z = 5:7:8 ie 14x/8y =5/7 ie 98x=40y then =49/20xz = 112/35x the ratio is x : 49/20x: 112/35x =20:49:64

34. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

A. Rs.7500 B. Rs.8000 C. Rs.8500 D .Rs.9000

Ans : Let B investment as x investment ratio =3500*12 :7x =2:3 ie 42000:7x =2:3 ie 14x=126000 then x =126000/14=9000

35. A and B entered into partnership with capitals in the ratio 4: 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:

A. Rs.330 B. Rs.360 C. Rs.380 D. Rs.430

Ans : capital ratio =4*3+4*3/4*7:5*3+5*4/5*7 ie 33:43 then A profit is33/76*760=330

36. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?

A. Rs.45 B. Rs.50 C. Rs.55 D. Rs.60

Ans : Ratio of oxen 70:60:45 ie 14:12:9 then C rent 9/35*175=45

37.A began a business with Rs.85,000. He was joined afterwards by B with Rs.42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

A. 4 months B. 5 months C. 6 months D. 8 months

Ans: 85000*12:42500x =3:1 ie 10200:425x =3:1 ie 1275x=10200, x=10200/1275=8

38. Arun, Kamal and Vinay invested Rs.8000, Rs.4000 and Rs.8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs.4005, then what will be the share of Kamal?

A. Rs.890 B. Rs.1335 C. Rs.1602 D. Rs.1780

Ans : Investment Ratio : 8000*6:4000*8:8000*8=48:32:64 ie 3:2:4 then B profit 2/9*4005=890

39. Renu started a software business by investing Rs.50,000. After six months, Harsitha joined her with a capital of Rs.80,000. After 3 years, they earned a profit of Rs.24,500. What was Renu’s share in the profit?

A. Rs.9,423 B. Rs.10,250 C. Rs.12,500 D. Rs.10,500

Ans: 50000*36:80000*30=180:240 ie 3:4 Renu profit 3/7*24500 =10500

40. A and B start a business jointly A invests Rs.16,000 for 8 months and B remains in the business for 4 months. out of total profit, B claims 2/7.how much money was contributed by B?

A. 10500 B. 11900 C. 12800 D. 13600

Ans: 128000:4x=5:2 ie 20x =256000 then x=12800

41. A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit be Rs. 27,000, C’s share is

A. Rs.8265 B. Rs.9000 C. Rs.10800 D. Rs 11250

Ans: let A investment as x then ratio of capital12x:2x*6:3x*4 ie 12x:12x:12x ie equal share . Each 9000

42. A, B and C enter into a partnership. A initially invests Rs.25 lakhs and adds another Rs.10 lakhs after one year. B initially invests Rs.35 lakhs and withdraws Rs.10 lakhs after 2 years C invests Rs.30 lakhs. In what ratio should the profits be divided at the end 3 years?

A. 10:10:9 B. 20:20:19 C. 20:18:19 D. none of these

Ans : 25*12+35*24:35*24+25*12:30*36 ie 1140:1140:1080 ie 114:114:108

43. A and B started a business with initial investments in the ratio 14: 15 and their annual profits were in the ratio 7: 6. If A invested the money for 10 months, for how many months did B invest his money?

A. 6 B. 7 C. 8 D. 9

Ans : 140:15x=7:6 ie 105x =840 then x=8

44. A, B, C hired a car for Rs.520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were:

A. 140 B. 160 C. 180 D. 220

Ans : the ratio of hire charges 7:8:11 for B 8/26*520=160

45. A and B start a business with investments of Rs.5000 and Rs.4500 respectively. After 4 months, A takes out half of his capital. After two more months, B takes out one-third of his capital while C joins them with a capital of Rs.7000. At the end of a year, they earn a profit of Rs.5080. Find the share of each member in the profit.

A) A - Rs.1400, B - Rs.1900, C - Rs.1780 B) A - Rs.1600, B - Rs.1800, C - Rs.1680 C) A - Rs.1800, B - Rs.1500, C - Rs.1780 D) A - Rs.1680, B - Rs.16000, C - Rs.1800

Ans : Ratio of share 50*4+25*8:45*6+30*6+70*6 ie 400:450:420 ie 80:90:84 each share of profit 80/254*5080 =1600; 90*20=1800;84*20=1680

46. Sekar started a business investing Rs.25, 000 in 1999, In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev’s share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?

A. RS 45000 B. RS 50000 C. RS 70000 D. none of these

Ans : 25*12+35*12+45*12: 35*24:35*12 = 1260:840:420 ie 3:2:1 Rajiv share 2/6*150000=50000

47. Three partners A, B, C start business. Twice A’s capital is equal to thrice B’s capital and B’s capital is four times C’s capital. Out of a total profit of Rs.16,500 at the end of the year. B’s share is:

A. RS 4000 B. RS 6000 C. RS 7500 D. RS 6600

Ans : let A caital is 100 then 200 :300:75 ie B share 300/575*16500

48. A, B and C enter into a partnership and their shares are in 1/2:1/3:1/4 ratio, After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B’s share?

A. Rs.129 B. Rs.144 C. Rs.156 D. Rs.168

Ans : ½*2+1/4*10:1/3*12:1/4*12 ie 14/4:12/3:12/4 ie 42:48:36 B share 48/126*378=144

49 .In a partnership, A invests 1/6 of capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C the rest of the capital for rest of the whole time. The total profit is RS 4600,B’s share is:

A. Rs.650 B. Rs.800 C. Rs.960 D. Rs.1000

Ans: 1/3:4/3:1/2*12 ie 1:4:18 then B share 4/23*4600=800

50) A man is standing on a railway bridge which is 180m long. He finds that a train crosses the bridge in 20seconds but himself in 8 seconds. Find the length of the train .

A. 120m B.140m C.240m D.200m

Sol: Let the length of the train be x meters, Then, the train covers x meters in 8 seconds and (x + 180) meters in 20 seconds. Therefore x/8 = (x+180)/20 ó 20x = 8(x+180) ó x = 120.Therefore Length of the train = 120m

51) If a man walks at the rate of 5kmph, he misses a train by only 7min. However if he walks at the rate of 6 kmph he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.

A. 6km B.8km C.7km D.None

Sol: Let the required distance be x km.Difference in the times taken at two speeds=12mins=1/5 hr.Therefore x/5-x/6=1/5 or 6x-5x=6 or x=6km.Hence ,the required distance is 6 km

52) From height of 8 mts a ball fell down and each time it bounces half the distance back. What will be the distance travelled

A. 24 B.32 C.40 D.None

Sol. 8+4+4+2+2+1+1+0.5+0.5+ and etc .. =24

53) Two trains 200mts and 150mts are running on the parallel rails at this rate of 40km/hr and 45km/hr.In how much time will they cross each other if they are running in the same direction.

Sol: Relative speed=45-40=5km/hr=25/18 mt/sec.Total distance covered =sum of lengths of trains =350mts.So, time taken =350*18/25=252sec.

54)Vivek travelled 1200km by air which formed 2/5 of his trip.One third of the whole trip , he travelled by car and the rest of the journey he performed by train. The distance travelled by train was ?

Sol: Let the total trip be x km.Then 2x/5=1200,x=1200*5/2=3000km

Distance travelled by car =1/3*3000=1000km

Journey by train =[3000-(1200+1000)]=800km.

55) What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?

**Answer**: 35392

Explanation : The number closest to 100 which is greater than 100 and divisible by 14 is 112, which is the first term of the series which has to be summed. The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series.112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392

56. The difference between the squares of two consecutive odd integers is always divisible by:

A. 3 B. 6 C. 7 D. 8

Ans : ie 1

^{2},3^{2},5^{2},7^{2}…… then 3^{2}-1^{2}=8 and next difference 16 and so on
Hence divisible by 8.

57. What largest number of five digits is divisible by 99?

A. 99909 B. 99981 C. 99990 D. 99999

Ans : 99990 is divisible by 99

58. If

*x*and*y*are the two digits of the number 653*xy*such that this number is divisible by 80, then*x*+*y*is equal to :
A. 2 B. 3 C. 4 D. 6

Ans : last digit should be 0 and last three digit should divisible by 8 ie 3x0 hence x may be 2

59. What least number must be subtracted from 13294 so that the remainder is exactly divisible by 97?

A. 1 B. 3 C. 4 D. 5

Ans : 97 | 13294 reminder 5 hence substract by 5

60. The difference between the numerator and the denominator of a fraction is 5.If 5 is added to its denominator, the fraction is decreased by 5/4.Find the value of fraction.

A. 1/6 B. 9/4 C. 13/4 D. 6

Ans: x-y =5 then x/y-5/4=x/5+y by substituting the value of A, B B is the correct answer

61.Find two numbers whose difference multiplied by the difference of their square is 160 and whose sum multiplied by the sum of their square is 580

Let x+y and x-y be the number ; 2y*4xy =160 – (1) 2x*{2(x

^{2}+y^{2})}=580(2)
8xy

^{2}=160 ie xy^{2}=20 –(1) but 4x^{3}+4xy^{2}=580 ie x^{3}+xy^{2}=145 ie x^{3}=145-20 then x=5 substitute x in xy^{2}=20 then y =2. Hence the required No 7 and 3
62.The sum of 5 consecutive odd number is 1185 what are the numbers?

Let 2x+1 is the smallest number 2x+1,2x+3,2x+5,2x+7,2x+9 =1185

Ie 10x+25 =1185 , 10x =1160 x =116

Then the numbers 233,235,237,239,241

63.Divide 28 into two such parts that the difference between their square is equal to 112.

Let x is the greatest part so the other part is 28-x and x

^{2}-(28-x)^{2}=112
(x+28-x)(x-28+x) =112 ie 28(2x-28)=112 ie x-14 =2 ie x=16. Hence the parts are 16,12

64.A certain number between 10-100 is 8 times the sum of its digits and if 45 is substracted from it the digits will be reverted

8(x+y) =10x+y ie 8x+8y=10x+y ie -2x+7y =0---(1)

10x+y-45=10y+x ie 9x-9y =45 ie x-y =5 ---(2)

By solving (1) and (2) 5y=10 ie y=2 x=7 the No is 72

65.The average of four consecutive even numbers is 27 find that numbers ?

2n+2,2n+4,2n+6,2n+8 ie 8n+20/4 =27 ie 8n+20 =108 n=4 then the numbers are 24,26,28,30

66).In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25.What is the value of fraction A?

A. 1/5 B. 1/25 C. 2/5 D. data inadequate

Ans : A is 2/5 and B is 1/5

67). Which of the following numbers is exactly divisible by 24?

A. 35718 B. 63810 C. 537804 D. 3125736

Ans : D it should be divided by both 3 and 8

68.The least number by which 72 must be multiplied in order to produce a multiple of 112, is :

A. 6 B. 12 C. 14 D. 18

Ans C 14 . 112 which is divisible by 14 .

69. A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:

A. 214 B. 476 C. 954 D. 1908

Ans : D

70. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the dividend is:

A. 4236 B. 4306 C. 4336. D. 5336

Ans D : 46*5 =230 divisor and quotient is 23 ie 1/10

^{th}of 230 then the number is 230*23+46=5336
71. A number when divided by 119 leaves 19 as remainder. If the same number is divided by 17, the remainder obtained is :

A. 2 B. 3 C. 7 D. 10

Ans 2 ie 119+19=138 by dividing this by 17 we will get reminder 2

72. The smallest number that must be added to 803642 in order to obtain a multiple of 11 is:

A. 1 B. 4 C. 7 D. 9

Ans C . It should be divisible by 11.Hence the adding of odd place digits

Substract with even place digits will give 0 ie 8+3+4-(0+6+9)

73. Find the number which is nearest to 457 and is exactly divisible by 11.

A. 450 B. 451 C. 460 D. 462

Ans D

74. In doing a division of a question with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is:

A. 0 B. 12 C. 13 D. 20

The number is 35x12=420 The correct quotient is 20

75. A boy multiplies 987 by a certain number and obtains 559981 as his answer. If in the answer, both 9's are wrong but the other digits are correct, then the correct answer will be:

A. 553681 B. 555181 C. 555681 D. 556581

Ans : C which is divisible by 987.

76. There is one number which is formed by writing one digit 6 times (e.g. 111111, 444444 etc.). Such a number is always divisible by:

A. 7 only B. 11 only C. 13 only D. all of these

Ans : B

77.A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by :

A. 7 only B. 11 only C. 13 only D. 1001

Ans B

78. How many three-digit numbers are divisible by 6 in all?

A. 149 B. 150 C. 151 D. 166

Ans : B and D it should be divided by both 2 and 3

79. A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is :

A. 1220 B. 1250 C. 22030 D. 220030

Ans D diff 555-445=110*2=220 as quotient and reminder 30 then the number is 220*1000+30=220030

80. 469157 x 9999 =?

A. 4586970843 B. 4686970743 C. 4691100843 D. 584649125

Ans : the first four 4691 then 10000-9157=0843 the last four digit 4691100843

PROBLEMS ON AGES

81. Father is aged three times more than his son Kavin. After 8 years, he would be two and a half times of Kavin's age. After further 8 years, how many times would he be of Kavin's age?

A. 2 times B. 5/2 times C. 11/4 times D. 3 times

Ans : Kavin age is x now after 8 years the fathers age 3x+8=5/2(x+8) ie x=24 another 8 years after son age 24+8+8 =40 fathers age 72+8+8=88 ie 11/5 times

82. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

A. 4 years B. 8 years C. 10 years D. None of these

Ans : x+x+3+x+6+x+9+x+12=5x+30 =50 ie x+6 =10 then x=4

83. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

A. 7 B. 8 C. 9 D. 10

Ans D: B+2+1/2(B)+B =27 ie 5B+4 =54 ie B =10

84. The ratio of the ages of mother to that of daughter is 7:3 today. After 5 years, this ratio would be 2:1. How many years old should the mother be at the time of birth of her daughter?

A. 18 B. 21 C. 22 D. 20

The age of ratio is now 7: 3 after 5 years 7+5=2(3+5)

85. The average age of class of 50 students is 24 years. If the average of 10 of them is 22 years, while average of another 10 is 26 years. What is the average of the remaining 30 students?

A. 22 B. 32 C. 24 D. 38

Ans : Toal years of 50 students =50*24=1200 the 30students average =1200-22*10-10*26/30 ie 720/30=24

86. If Jude was 1/3rd as old as John 5 years back and Jude is 17 years old now, How old is Jude now?

A. 40 B. 41 C. 36 D. 48

Ans : Now John age x 5 years x-5 =3(17-5) ie x-5 =36 x=41

87. The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

A. 12 years B. 14 years C. 18 years D. 20 years

The age of son is 60-(60-12) =12 after 6 years the age of son =18

88.Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A. 16 years B. 18 years C. 28 years D. 24.5 year

X: X-7 = 7:9 ie 9X =7X-49 ie 2X =49 X =24.5

89. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?

A. 12 years B. 15 years C. 19 and half D. 21 years

Ans B ; present year of Arun is 26-6=20 deepak age 5*3 =15

90. The Average age of a class of 22 students in 21 years. The average increases by 1 when the teacher’s age also included. What is the age of the teacher?

A. 44 B. 43 C. 41 D. 40

Ans A ; 22*21=462 23*22=506 the diff is 44

91. The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2: 3: 4. What is the present age of Saransh?

A. 24 Years B. 32 Years C. 34 Years D. 38 Years

92. Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was the ratio of their ages 3 : 5?

A. 5 Years B. 10 Years C. 20 Years D. 37 Years

93. 15 years hence, Rohit will be just four times as old as he was 15 years ago, How old is Rohit at present?

A. 20 B. 25 C. 30 D. 35

94. If twice the son’s age in years be added to the father’s age, the sum is 70 and if twice the father’s age is added to the son’s age, the sum is 95. Father’s age is:

A. 40 Years B. 35 Years C. 42 Years D. 45 Years

95. The total age of A and B is 12 year more than the total age of B and C. C is how many years younger that A?

A. 12 B. 24 C. C is elder than A D. none of these

Ans : C is older than A ;A+B+12=B+C ie A+12=B

96. A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?

A. 18 Years B. 20 Years C. 24 Years D. 32 Years

97. Five years ago Mr. Mohanlal was thrice as old as his son and five years after he will be twice as old as his son. Mr. Mohanlal’s present age (in years) is

A. 35 B. 45 C. 50 D. 55

Ans : A ;

AVERAGE

98. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

A. 6.25 B. 6.5 C. 6.75 D. 7

Ans : The required run rate =282-3.2*10/40=6.25

99. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

Ans: The average age of family =67*2+35*2+6*3/7=134+70+18/7=224/7=32

100. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

A. 0 B. 1 C. 10 D. 19

Ans : all are 0

101. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A. 76 kg B. 76.5 kg C. 85 kg D. Data inadequate

Ans : increase 8*2.5+age of out goer 65= 85

102. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A. 23 years B. 24 years C. 25 years D. None of these

Ans : let average age of team x then 9(x-1)= 11x-55 ie 9x -9 =11x -55 ie 2x=46 then x=23

103. The average monthly income of P and Q is Rs.5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs.5200. The monthly income of P is:

A. 3500 B. 4000 C. 4050 D. 5000

Ans (q+r)/2 =6250 ie q+r =12500 (r+p)/2=5200 ie r+p =10400 again p+q =10100

By 1 &2 q –p = 2100 ie p-q =-2100 then 2p =8000 p=4000

104. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

A. 35 years B. 40 years C. 50 years D. None of these

Ans : C the present total age of 3 is 90 and total age of wife and child is 40 then husband age is 90-40=50

105. A car owner buys petrol at Rs.7.50, Rs.8 and Rs.8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs.4000 each year?

A. Rs.7.98 B. Rs,8 C. Rs.8.50 D. Rs.9

Ans B the average cost 7.50+8+8.50/3=8

106. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

A. 17 kg B. 20 kg C. 26 kg D. 31 kg

Ans : A+B =80 B+C =86 A+2B+C =166 but A+B+C =135 by substracting B = 31

107. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.

A. 47.55 kg B. 48 kg C. 48.55 kg D. 49.25 kg

Ans : 16*50.25+8*45.15/24=48.55

108. A team of 8 persons joins in shooting competition , the best marks man scores 85 , if he had scored 92 points then the average would have been 84 . The number of points the team scored is

A) 665 B)655 C)675 D) None

Ans: The total score by team is (84x8)-7(ie 92-84) =672-7=665

109. The average of 5 numbers is 27 , if one excluded then 25 what is the number excluded

A) 35 B)25 C )45 D)None

Ans : The excluded number is (27x5)-(25x4) =35

110. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

A. 250 B. 276 C. 280 D. 285

Ans : Sunday 1,8,15,22,29 hence (5*510+25*240)/30=285

111. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:

A. 10 B. 20 C. 40 D. 73

Ans : for ½ increase the marks raising 20 hence the total no be 20*2=40

112. The average of all odd numbers up to 100 is:

A. 51 B. 48.5 C. 50 D. 49.2

Ans : Sum of all odd numbers =

113. In travelling from city A to city B, John drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was his average speed for the whole trip?

A. 50 B. 53.5 C. 55 D. 56 E. 57.5

Ans : total travel 1*50+3*60=230mph then average 230/4=57.5

RATIO AND PROPORTION

114. The salaries of A, B, C are in the ratio 2 : 3 : 5. if the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?

A. 3:3:10

B. 10:11:20

C. 23:33:60

D. none of these

Ans : new salary are 2:3:5 multiply by increment ratio 3:2:4 ie 6: 6:20 ie 3:3:10

115. Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it (in kgs)?

A. 58

B. 60

C. 64

D. 70

Ans C ; the weight of copper =28.8/9*11=35.2 hence total weight is 64

Prepared by O. MADHAVARAJ |

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