ARITHMETIC ABILITY 4

Thursday, April 29, 2010

Read the questions carefully and pick the correct answer.

1.
A sum of money becomes 30 / 14 times itself in 10 years. The rate of S. I. Is
A.
11.4 %

B.
15 %
C.
12.3 %
D.
14.5 %
Answer & Explanation
Answer: Option A
Explanation:
X + X * R * 10 / 100 = 30X / 14X + 10RX / 100 = 30X / 14100X + 10RX / 100 = 30X / 14X (100 + 10R) / 100= 30X / 14100 + 10R / 100= 30 / 141400 + 140R= 3000140 = 1600R= 1600 / 140= 11.4%

2.
A buys an orange from B for Rs 4 and sells it to c for Rs. 8. He later buys the orange back from c for Rs. 12 and sells it to B for Rs 16. What is his profit over the venture.
A.
Rs. 8

B.
Rs. 4
C.
Rs. 24
D.
No profit
Answer & Explanation
Answer: Option A
Explanation:
There are 2 different transactionsIn 1st transaction profit = Rs. 4In 2nd transaction profit = Rs. 4Total profit = Rs. 8

3.
A buys Sugar at Rs. 20 per kg and prices it so as to earn a profit of 20%. However his balance is Faulty and shows 800 gms when it is actually 1000 gms. What is his actual profit margin.
A.
24 %

B.
20 %
C.
15 %
D.
12 %
Answer & Explanation
Answer: Option A
Explanation:
A prices Sugar at Rs. 24 per kg.He sells 1000 gm for sale price of 800gm. = 24 * 4 /5 = 96 / 5 = 19.2Actual profit margin = 4.8 * 100 / 20 = 24.0%

4.
2, 10, 28, 54,____
A.
88

B.
80
C.
101
D.
62
Answer & Explanation
Answer: Option A
Explanation:
The series is as follows, 2, 2*4+2, 4*6+4, 6*8+6, 8*10+8.

5.
The monthly expenses at IIM are partly constant and partly vary directly as the no. of inmates. If the expenses are Rs 4000 when no. of inmates is 240 and Rs 3200 when no. of inmates is 200 . Then no. of imnates when expense is Rs 3760 are
A.
148

B.
135
C.
128
D.
156
Answer & Explanation
Answer: Option A
Explanation:
Let x = variableY = fixed expense240x + y = 4000200x + y = 320040x = 800x = 800 / 40 = 20y = 800Let x = no. of inmates20x + 800 = 376020x = 2960x = 2960 / 20 = 148

6.
How much of 200 Rs / kg type tea should be mixed with 12 kg of 100 Rs / kg type tea to make 160 Rs / kg of branded tea ?
A.
18

B.
20
C.
25
D.
32
Answer & Explanation
Answer: Option A
Explanation:
Let amount be X kg200x + 100 * 12 / x + 12 = 160200x + 1200 = 160x + 192040x = 720x = 72 / 4 = 18

7.
After selling a chain Ram found that he had made a loss of 20% had he sold it for Rs 54 more, he Would have made a profit of 10% his the actual loss was
A.
Rs. 36

B.
Rs. 30
C.
Rs. 18
D.
Rs. 50
Answer & Explanation
Answer: Option A
Explanation:
30% of C.P. of chain = Rs. 54 20% of C.P. = Rs 54 * 20 / 30= Rs 36

8.
What is 1.99 * 2.01/0. 001
A.
3.9999
B.
398.99
C.
3989.9
D.
None of these

Answer & Explanation
Answer: Option D
Explanation:
1.99 * 2.01 = ( 2 - 0.01) ( 2 + 0.01 )= 4 - 0.001 = 3.9999Ans. 3999.9

9.
Complete the series 12, 24, 48, 96, _____
A.
192

B.
256
C.
26
D.
88
Answer & Explanation
Answer: Option A
Explanation:
( 96 * 2 )

10.
4 , 9, 25, 49, _____
A.
64
B.
81
C.
100
D.
121

Answer & Explanation
Answer: Option D
Explanation:
Series is square of prime nos.Hence 112 = 121

11.
A shopkeeper marks his goods to make a profit of 25%. But he allows 5% discount for cash payment. His profit on a cash transaction is
A.
19.25
B.
21.5
C.
18.75

D.
20
Answer & Explanation
Answer: Option C
Explanation:
Let the C.P. of the goods be 100He marks them at 125Cash discount = 5% of 125= 6.25= 125 - 6.25= 118.75 - 100 = 18.75

12.
If we divide 444 in 3 parts such that 2 times the first is equal to 4 times the second and 9 times the Third then the three parts are in the ratio:
A.
(1/2) : (1/4) : (1/9)
B.
2: 4: 9

C.
9:4:2
D.
None of these
Answer & Explanation
Answer: Option B
Explanation:
2I : 4II : 9IIISo I : II : III = 1 / 2 : 1 /4 : 1 / 9

13.
The length, breadth and thickness of a rectangular object are in the ratio 1:2:3 and its whole Surface area is 696 sq. cm. What is the length
A.
10 cm
B.
5 cm

C.
15 cm
D.
20 cm
Answer & Explanation
Answer: Option B
Explanation:
Length : Breadth : Thickness1 : 2 : 3Let length = x, Breadth = 2x and thickness = 3xWhole surface area = 2 [ ( 2 * 2x) + ( 2x * 3x) + ( 3x * x)]2[2x2 + 6x2 + 3x2 ] = 4x2 + 12x2 + 6x222x2 = 550 = x2 = 550 / 22 = 25x = 5 Length x = 5 cm

14.
A man is 40 years old and has 5 brothers born at equal intervals. The sum of the age of the man and brother is 180. What is the age of the eldest brother if the youngest is 4 years old.
A.
37 years
B.
42 years
C.
68 years

D.
72 years
Answer & Explanation
Answer: Option C
Explanation:
Father's age = 40age of sons = 180 - 40 = 140Age of the youngest = 4 age of the fourth = 4 + xage of third = 4 + 2xage of second = 4 + 3xage of first = 4 + 4x\ 4 + 4+x + 4+2x + 4+ 3x + 4+ 4x = 18020 + 10x = 18010x = 160x = 16Eldest = 4 + 4 * 16= 64 + 4 = 68 Years

15.
Ashish has x Chocolates, First he gave y chocolates Amit. Then he gave 1 / 4 of what was left to Amrish. How much chocolates did Ashish have in the end.
A.
1 / 2(x - y)
B.
x -y
C.
3 / 4 ( x-y)

D.
1 / 4 ( x - y)
Answer & Explanation
Answer: Option C
Explanation:
Ashish had x marblesAfter he gave y marbles to Amit he had x - yOut of x - y he gave 1 / 4 to Amrishhe has 3 / 4 ( x - y ) left with him

16.
A ball is dropped gently from a height of 100 Mts. After striking the floor it rebounds 4 / 5 of the Height from which it has fallen and continues this way and stops finally. The total distance travelled by the ball is _________ Mts.
A.
900 mts

B.
1000 mts
C.
1200 mts
D.
860 mts
Answer & Explanation
Answer: Option A
Explanation:
Total distance = 100 + 2 (100) ( 4 / 5) + 2 [ 100 * (4 / 5)2 + ----2]= 100 + 200 [ 4 / 5 + ( 4 / 5 )2 + ( 4 / 5 )3 -----2]= 100 + 200 * (4 / 5) / ( 1 / 5)= 100 + 800 = 900 mts.

17.
If the probability that A will live 10 years is 5 / 6 and B will live 10 years in 7 / 8 what is the Probability that both will live after 10 years ?
A.
1/12
B.
35/48

C.
61/23
D.
49/79
Answer & Explanation
Answer: Option B
Explanation:
The probability that both will live after 10 years is 5 / 6 * 7 / 8 = 35 / 48

18.
What is the probability of obtaining a total of 10 points in a single throw with two dice.
A.
1/10
B.
1/13
C.
1/18

D.
2/17
Answer & Explanation
Answer: Option C
Explanation:
Dice I
Dice II
4
6
6
4probabilities = 2 / 36 = 1 / 18

19.
Suppose 10 teachers are required in a college. If 4 are M.A's and 10 doctorates apply for the Professorship, how many selections can be made taking all MA's
A.
210

B.
222
C.
340
D.
720
Answer & Explanation
Answer: Option A
Explanation:
All the 4 MA's have to be selected6 choices are leftHence 10 c6 = 210

20.
How many squares can be formed by joining the points of a decagon ?
A.
130
B.
110
C.
120
D.
105

Answer & Explanation
Answer: Option D
Explanation:
A square is formed by 4 points on the same plane= 10 c4 = 10 * 9 * 8 * 7 / 4 * 3 * 2 = 105

21.
In 40 litres of a mixture of milk and water, the ratio of the constituents in the above order is 6:4.To make their ratio 4:6, ________ litres of water must be added to the mixture.
A.
10
B.
20

C.
30
D.
40
Answer & Explanation
Answer: Option B
Explanation:
In 40 liters milk and water = 6x : 4x* 40 / 10 = 24 lts of milkand 16 lts of waterso if milk = 4y = 24 ltswater = 6y = 36 lts.additional liters of water = 36 - 16 = 20 lts.

22.
If the price of sugar rises by 10 per cent, a householder must reduce his consumption of sugar by _________Percent so as not to increase his expenditure.
A.
12.5
B.
15
C.
9

D.
20
Answer & Explanation
Answer: Option C
Explanation:
Price x quantity = Expense1. P P * Q1 = P * QQ1 = Q / 1.1Decrease = Q - Q / 1.1 = .1 Q / 1.1 = 1Q / 11= 9.1 %

23.
In a college, there are 200 students in class XI, 250 in class X and 350 in class IX. The enrolment percentage of class XI is ____________ per cent of the total of all three classes.
A.
20
B.
20.5
C.
25

D.
30
Answer & Explanation
Answer: Option C
Explanation:
Total students = 200 + 250 + 350 = 800Therefore enrolment % of class 11 = 200 * 100/ 800= 25 %

24.
12, 18, 30 litres are to be drawn from three vessels respectively. What is the exact capacity of measure which will do it most quickly ?
A.
6 litre

B.
7 litre
C.
8 litre
D.
11 litre
Answer & Explanation
Answer: Option A
Explanation:
H.C.F. of 12, 18 and 30= H.C.F. of 12 = 22 * 318 = 32 * 230 = 2 * 3 * 5= 2 * 3 = 6 lts.

25.
Hari singh sold 1/4 of his estate, gave 2/3 of the remainder to his son and 1/3 of the balance to his daughter. His daughter's share values Rs. 7,000. The value of the whole estate is
A.
Rs. 84,000

B.
Rs. 25,000
C.
Rs. 75,000
D.
Rs. 1,50,000
Answer & Explanation
Answer: Option A
Explanation:
Let Hari's Estate value = xHe sold = 1 / 4 xHis son's share = 2 / 3 * 3x / 4 = (1/2) xBalance = x - 1x / 4 - 1x / 2 = 1x / 4He gave his daughter 1x / 4 * 1 / 3 = 1x / 12His daughters estate value = 70001x / 12 = 7000x = 7000 * 12 / 1Rs. = 84000

26.
A man after allowing a trade discount of 20% from the marked price, makes a profit of 10%. His marked price will be
A.
27% above cost price
B.
7% above cost price
C.
30% above cost price

D.
None of these
Answer & Explanation
Answer: Option C
Explanation:
Let MP = x SP = 0.8xSP - CP = 110 / 100 cp0.8x = 110 / 100 cpx = 110 /100 * 0.8 = 110 / 80 = 11 / 8 = 1.3 of cp= 30 %

27.
1,250 mangoes were distributed among a group of children. Each child got twice as many mangoes as the number of boys in the group. The number of children in the group was...
A.
25

B.
45
C.
50
D.
625
Answer & Explanation
Answer: Option A
Explanation:
Let NO. of children = XEach child gets 2x mangoes2x2 = 1250x2 = 625x = 25

28.
A vendor sells 20 apples for a Rupee gaining there - by 50%. How many oranges did he buy for a Rupee ?
A.
30

B.
12
C.
14
D.
16
Answer & Explanation
Answer: Option A
Explanation:
SP - CP = Profitprofit % = SP - CP / CP * 10050 = SP - CP / CP * 100CP = SP - CP / 50 * 100CP = 2 SP - 2 CP3 CP = 2 * Re.13 CP = 2CP = 2 /3CP of 20 apple = RS. 2 / 3= Re 120 * 3 / 2= 30 Apples

29.
If no income-tax is charged on the first Rs. 3,000 of the income, how much does a man pay as income-tax at 3 P in the rupee, if his total income is Rs. 5,000 ?
A.
Rs. 60

B.
Rs. 90
C.
Rs. 9
D.
None of these
Answer & Explanation
Answer: Option A
Explanation:
0.03 * 2000 = RS 60

30.
A wholesaler allows a discount of 10% on cash payment. The value of the article for which the customer paid Rs. 180 is
A.
Rs. 212
B.
Rs. 188
C.
Rs. 200

D.
None of these
Answer & Explanation
Answer: Option C
Explanation:
90 % = 180100 % = 180 * 100 / 90 = Rs 200

31.
A worker earns twice as much in May as in each of the other months. What part of the entire year's earnings does she earn in May ?
A.
2/13

B.
2/11
C.
1/6
D.
4/13
Answer & Explanation
Answer: Option A
Explanation:
Let x be the monthly earning yearly earning = 13xEarning in May = 2xRequired fraction = 2x / 13x = 2 / 13

32.
During one year the population o f a town increased by 20% and during the next year it diminished by 20%. Then the population now is
A.
Same as in the beginning
B.
Greater than that in the beginning.
C.
Less than that in the beginning

D.
None of the above
Answer & Explanation
Answer: Option C
Explanation:
Let the population in the beginning be 100After increase population = 120After decrease population = 120 * 20 / 100 = 24After decrease population = 120 - 24 = 96

33.
A garrison of 600 men had provisions for 20 days. However, reinforcement of 800 men arrived. The food will now last for
A.
18 days
B.
15 days

C.
17.5 days
D.
16 days
Answer & Explanation
Answer: Option B
Explanation:
600 Men --> 20 day1 man --> 20 * 600 days800 men --> 20 * 600 / 800 = 15 days

34.
A is 5 km. ahead of B. The speeds of A and B are 2 and 3 km/hr respectively. B will over take A in
A.
5 hour

B.
1 hour 20 minute
C.
4 hour
D.
48 minute
Answer & Explanation
Answer: Option A
Explanation:
Let t be the time takenDistance covered by both in time t will beA = 2t and B = 3t3t = 2t + 5t = 5 hours

35.
Nitin drives his car to his office at aspeed of 50 km/h. And returns along the same route at a speed of 70 km/h. His average speed for the entire round trip is ______km/h.
A.
58.3

B.
68.6
C.
54
D.
None of above
Answer & Explanation
Answer: Option A
Explanation:
Average speed = 2 * 50 * 70 / 50 + 70 = 7000 / 120 = 350 / 6= 58.3 Km / hr.