ARITHMETIC ABILITY 2

Thursday, April 29, 2010

Read the questions carefully and pick the correct answer.

1. Suman borrowed Rs. 60,000 to build a bungalow. She pays 10 % S.I. She lets out her bungalow and receives a rent of Rs. 1500 p.m. In how many years will she clear her debt.
A.1 year
B.4 years
C.5 years
D.2 years

Answer: Option C
Explanation:
S.I = 60,000 * (10/100)= Rs. 6000Rent received = 1500 * 12= 18000Therefore debt cleared in one year = 18000 - 6000=12000Therefore in 5 years.

2. If the interest on Rs. 800 exceeds that on Rs. 600 by Rs. 15.50 in 6 months, find the rate percent p.a.
A.15.5%
B.18.5%
C.14%
D.5%

Answer: Option A
Explanation:
800 - 600 = 200n = 6 months. = 1 /2 yearr = 100 I /Pn= 100 * 15.50/ 200 * 1/2= 1550 / 100= 15.5%

3. Find the compound interest in Rs.2400 for 2 1/2 years at 5 % p.a.,interest being compounded annually.
A.270.50
B.300
C.412.25
D.312.15

Answer: Option D
Explanation:
A = P ( 1 + r/ 1002 ( 1 + r /100)= 2400 ( 1+ 5 /1002 ( 1 + 2 1/2/100)= Rs. 2712.15Therefore C. I. = 2712.15 -150; 2400= Rs. 312.15

4. A square piece of ground is 45 metres long. Find the cost of fencing it round with 10 lines of wire at the rate of Rs. 1.50 per metre.
A.2700
B.2500
C.2300
D.2800
Answer: Option A
Explanation:
Perimeter of square = 4a = 4 * 45=180 mLength of fence = 10 * 180=1800m. with 10 lines of wire.Therefore cost of wire = 1.50 * 1800= Rs. 2700

5. The external dimensions of a box are 10 cm , 6 cm , and 4 cm. If the thickness of wood is 1 cm, Find the volume of wood.
A.125
B.150
C.176
D.183

Answer: Option C
Explanation:
External volume = l * b * h= 10 * 6 * 4= 240 cm3Internal dimensions = ( 10 -2); ( 6- 2); ( 4- 2)= 8 , 4 , 2 cm.Internal volume = 8 * 4 * 2= 64 cm3Therefore volume of cube = 240 - 64= 176 cm3

6. The radii of two cylinders are in the ratio 2 : 3 and heights 5 : 3. Calculate ratio of their volumes.
A.20/27
B.27/20
C.3/4
D.20/32

Answer: Option A
Explanation:
Let radii --> 2x and 3xLet height --> 5y and 3yV1 /V 2= ( 22 /7 ) ( 2x ) 2 ( 5 y ) / ( 22 /7 ) ( 3x ) 2 ( 3y )= 20 / 27

7. The diameter of a roller. 100 cm long is 60 cm. It takes 500 complete revolutions to level a playground. What is the cost of levelling at 50 ps. per sq. m.
A.200
B.220
C.400
D.500

Answer: Option B
Explanation:
Diameter of a roller = 60 cmr = 30 cm = 0.30 mHeight of roller = 1.00 mCurved surface area = 2 ( 22 / 7 ) rh= 2 * ( 22 / 7 ) * 0.30 * 1= 1.32 / 7= 0.88Area covered by roller = 500 * 0.88= 88 * 5= 440 cm2Therefore cost of levelling = 0.50 * 440=5 * 44= 220

8. If a+b+c = 0.The value of a4+b4+c4/b2c2+c2a2+a2b2 is :
A.2
B.3
C.6
D.8

Answer: Option A
Explanation:
Since a+b+c = 0a+b = -c(a+b2=(-c2)a2+2ab+b2=c2a2+b2-c2= -2ab(a2+b2+c2) 2=(-2ab) 2or a4+b4+c4+2a2b2-2b2c2-2c2a2=4a2b2ora4+b4+c4=2a2b2+2b2c2+2c2a2or=2(a2b2+b2c2+c2a2)a4+b4+c4/a2b2+b2c2+c2a2= 2

9. A man divides his property among his sons so that one gets half another gets quarter and third gets one fifth and the fourth Rs. 10000. What is the value of the total property?
A.200000
B.400000
C.1400000
D.2400000
Answer: Option A
Explanation:
Let x be the total value of the property.x = x/2+x/4+1/5x+10000= (10+5+4)x/20+10000= 19x/20+10000= 20*10000= 200000

10. If m:n = 2:3, the value of 3m+5n/6m-n is
A.7/3
B.3/7
C.5/3
D.3/5

Answer: Option A
Explanation:
m/n = 2/33m = 2nnow, 3m+5n/6m-n = 2n+5n/4n-n = 7n/3n = 7/3

11. Divide 27 into two parts so that 5 times the first and eleven times the second are together equal to 195
A.17:10
B.15:11
C.16:10
D.10:17

Answer: Option A
Explanation:
a+b = 275a+11b = 195solving simultaneously we have,a = 17 b = 10


12. 40% of 5/6 is
A.1/3
B.2/3
C.2/6
D.3/4

Answer: Option A
Explanation:
40% of 5/6 = 40/100*5/6 = 1/3

13. A dog taken 4 leaps for every 5 leaps of a hare but three leaps of the dog is equal to 4 leaps of the hare. Compare their speeds.
A.16:15
B.12:16
C.19:20
D.10:12

Answer: Option A
Explanation:
3 leaps of the dog = 4 leaps of the hare.1 leap of the dog = 4/3 leaps of the hare.4 leaps of the dog = 16/3 leaps of the hare.Speed of the dog : Speed of the hare16: 15

14. 55 men can finish a job in 42 days. If the work has to be completed 9 days earlier, how many additional men must be engaged to complete the work?
A.15
B.20
C.25
D.12

Answer: Option A
Explanation:
9 days earlier mean that the work should be completed in (42-9) = 33 days.No. of Men = 42*55/33 = 70Hence the no. of extra men = 70-55=15 men

15. A retailer buys an electronic buzzer for Rs. 215. His overhead expenses are Rs. 25. If he sells the buzzer for Rs. 300, his profit percentage would be
A.25%
B.26%
C.20%
D.30%

Answer: Option A
Explanation:
Total cost of the electronic buzzer = Rs.215+Rs.25 = Rs.240Selling Price = Rs.300Profit% = 60/240*100 = 25%


16. In an election between two candidates one got 55% of the total valid votes. 20% of the votes are invalid. If the total votes are 7500, what is the number of valid votes that the other person got?
A.2700
B.2800
C.3000
D.3300

Answer: Option A
Explanation:
7500*20%=1500No of valid votes=600045% of 6000=2700

17. Aunt uses a car to travel from mumbai to nashik. She travelled at 60 kmph and covered half the distance in 2 hours. At what uniform speed should she travel to reach nashik at 4.00 pm?
A.40
B.60
C.50
D.35

Answer: Option A
Explanation:
At the speed of 60 kmph, aunt will reach nashik in 4 hours. The distance between mumbai and nashik is 240 kms.If 120 km are to be covered in 3 hours then aunt should travel at the uniform speed of120/3 = 40kmph

18. The sum of ages of Nitya and her aunt is 63 years. Four years ago her aunt's age was 4 times that of Nitya's ages at that time. What is the present age in years of Nitya's aunt?
A.48
B.50
C.45
D.40

Answer: Option A
Explanation:
If x and y are the ages of Nitya and Nitya's aunt,x+y = 63y-x = 4(x-4)we have Nitya's age = 15 yearsher aunt's age = 48 years

19. A watch ticks 90 times in 95 secs. And another watch ticks 315 times in 323 secs. If they start together, how many times will they tick together in first hour?
A.101 times
B.100 times
C.99 times
D.102 times

Answer: Option A
Explanation:
First watch ticks after 95/90 seconds. second watch after 323/315 seconds.LCM = 19*5*17/45 seconds.No. of times they will tick in first 3600 seconds = 3600/(19*5*17)/45 Once they have ticked together in the begining , 50 in 1 hour they tick 100+1 = 101 times

20. Area of a square is given to be S. If the sides are doubled, then the new area will be
A.4S
B.2S
C.S/2
D.S2

Answer: Option A
Explanation:
If area = S, Sides = sqrt(S)If side is doubled i.e. 2sqrt(S)area = {2sqrt(S)}2= 4S

21. The product of two numbers is 2400. If the bigger number is 1.5 times the smaller number is
A.40
B.45
C.35
D.30

Answer: Option A
Explanation:
Let a and b be the numbers where b is the bigger number.b =3/2aa * b = 2400(given)3/2a2= 2400a2= 1600a = 40

22. Six men earn as much as 8 women, 2 women earn as much as 3 boys and 4 boys earn as much as 5 girls. If a girl earn Rs.50 a day, then the earning of a man would be
A.Rs. 125
B.Rs. 135
C.Rs. 105
D.Rs. 120

Answer: Option A
Explanation:
6 M = 8W, 2W = 3B, 4B = 5G1 G = Rs. 50 a day.Now, 1B = 5/4G 1 W = 3/2 * 5/4G1 M= 8/6* 3/2* 5/4G = 5/2G1 M = 5/2 * 50 = 125/-Rs.

23. A train 150 meters long running at a speed of 60 kmph takes 30 seconds to cross a bridge. The length of the bridge is,
A.350m
B.450m
C.300m
D.400m
Answer: Option A
Explanation:
The distance covered by the train in 30 seconds = 6000/3600* 30 metres= 500 metres.Length of the Bridge = 500 - 150= 350m.

24. The cost of painting the walls of a hall 30 meters long, 20 meters broad and 12 meters high, if it costs 25 paise per sq. metre.
A.Rs. 300
B.Rs. 325
C.Rs. 350
D.Rs. 400

Answer: Option A
Explanation:
Area of the four walls.= 2(length + breadth ) * height= 2 (30 + 20 ) *12 sq. meteres= 1200 sq. metresTotal cost of painting = Rs. 1200*12/100= Rs.300

25. The product of 3sqrt(4), 6sqrt(6) and 2sqrt(5) is
A.6sqrt(12000)
B.6sqrt(1000)
C.4sqrt(12000)
D.3sqrt(120000)
Answer: Option A
Explanation:
Product of 3 sqrt (4), 6 sqrt (6), 2 sqrt (5) is4 1/3 * 6 1/6 *5 1/2=42/6 * 61/6 * 53/6=(42 * 6 * 53)1/6=( 16 *6 *125)1/6= 6 sqrt(12000)

26. If A can complete a work in 6 hours, and B can complete it in 8 hours, then how much time would they take to complete the work together?
A.3(3/7)
B.2(5/2)
C.4(5/6)
D.None of these

Answer: Option A
Explanation:
A takes 6 hours to complete a work.He can complete 1/6th of the work in one hour.(taking complete work as 1.)B takes 8 hours to complete it.He can complete 1/8th of the work in one hour.Together, A and B can complete,1/6+1/8 = 14/48 = 7/24 of the work.
Hour
Work
1
7/24
?
24/24=24/7= 3 (3/7)

27. A,B,and C can independently complete a task in 6,8 and 12 hours respectively. C starts working. 2 hours later she stops and simultaneously A and B starts working. Yet another 2 hours later, B stops working too. Now how long does A have to work alone to complete the task?
A.3 hours
B.6 hours
C.8 hours
D.1.5 hours

Answer: Option D
Explanation:
In one hour, C can complete 1/12th of the work.In two hours, he can complete 1/12*2 = 2/12th of the work.A and B start work simultaneously,together work completed by A and B,1/6+1/8 = 14/48 work = 7/24 work.In 2 hours they complete 7/24*2 = 7/12 workTotal work done by A,B,C = 7/12+2/12 = 9/12Total work to be completed = 12/12 or 1Remaining work = 3/12
Hour
Work done by A
1
1/6
?
3/123/12*6 = 1.5 hours

28. 128, 32, 224, 56, ____
A.392
B.350
C.25
D.36

Answer: Option A
Explanation:
/4, *7-----NOT CLAER------

29. Taps A and B can independently fill a tank in 6 and 10 hours . Leak C can empty a filled tank in 8 hours. On an empty tank A, B, C are opened. How long does it take to fill the tank?
A.7.05
B.8.05
C.10.10
D.5.07

Answer: Option A
Explanation:
In 1 hour C can empty 1/8th of tankIn 1 hour amount of water filled in the tank = A+B-C= 1/6+1/10-1/868/480 = 17/120
Hour
Water filled in tank
1
17/120
?
120/120= 120/17 = 7.05 hours

30. Ten years ago, Ram was 2/3 Shyam's age. 10 years hence Shyam will be 25% older than Ram. What are their present ages?
A.30:40
B.40:30
C.20:40
D.30:60

Answer: Option A
Explanation:
Let the present ages of Ram and Shyam be R and S resp.3R-2S = 10 -- I4S-5R = 10 -- II15R-10S = 50-15R+12S = 302S = 80S = 40R = 30Hence 30:40

31. 25 years ago A's age was 1/3 of what B's age will be 25 years hence 50 years hence, B's age will be twice A's present age. What is the sum of their present ages?
A.90
B.100
C.200
D.400

Answer: Option B
Explanation:
Let their present ages be A and B.3A-B = 100 -- I2A-B = 50 -- II3A-B = 100-2A-B = 50A = 50B = 50Sum of their ages = A+B=100

32. The sum of X and Y's age is 105. When X was Y's age, she was 1.5 times Y's age then what are their present ages?
A.45:60
B.30:40
C.50:60
D.60:45

Answer: Option D
Explanation:
Let their present ages be X and Y.X+Y = 105 --I1.5X-2Y = 0 --IIX = 60Y = 45Hence 60:45

33. 10 men working for 20 days, 5 hours a day can build a fence of length 20 meters. I need to build a fence of length 100 metres in 5 days and the men are willing to work 10 hours a day. How many men do we need?
A.200
B.300
C.400
D.100

Answer: Option D
Explanation:

M
D
H
L
Old
10
20
5
20
New
x
5
10
10010/x = 5/20*10/5*20/100x = 100

34. Find the factor of a4+64
A.(a2+8)(a2-8)
B.(a2+2)(a2-2)
C.(a2+4a+8)(a2-4a+8)
D.None of these

Answer: Option C
Explanation:
a4 + b4 = (a2+ab+b2)(a2-ab+b2)=(a2+4a+8)(a2-4a+8)=(a2+8)2-(4a)2=a2 + 64

35. A contractor undertakes to complete a project in 56 days using 100 men. However after 46 days, 100 men thereby completing the project on time. Had the additional men not been deployed, then by how many days would the project be delayed?
A.10
B.20
C.5
D.40

Answer: Option A
Explanation:
x = 10*2 = 20 days100 men would require 20 days from 46 days46+20 = 66 daysBut we want to complete the work in 56 days.so 10 days