Aptitude

1

What is the value of c , If 8 is 4% of a, and 4 is 8% of b. c equals b/a.

a

12

b

1/4

c

0.155

d

None of these

Let be the 4% of a is 4a/100.

Since this equals 8, we have 4a/100=8.

Solving for a yields a=8×(100/4)=200.

Also, 8% of b equals 8b/100, and this equals 4.

Hence, we have (8/100)×b=4.

Solving for b yields  b = 50.

Now, c=b/a=50/200=1/4.

2

Half percent, written as a decimal, is

a

0.2

b

0.02

c

0.005

d

0.05

As we know, 1% = 1/100
Hence, (1/2)% = (1/2 * 1/100) = 1/200 = 0.005

3

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?

a

20

b

30

c

40

d

50

The fruit content in both the fresh fruit and dry fruit is the same.

Given, fresh fruit has 68% water. So remaining 32% is fruit content. Weight of fresh fruits is 100kg

Dry fruit has 20% water. So remaining 80% is fruit content. Let weight of dry fruit be y kg.

Fruit % in freshfruit = Fruit% in dryfruit

$\inline \fn_cm \therefore$(32/100) ** 100 = (80/100 ) ** y

We get, y = 40 kg

4

A shepherd has 1 million sheep at the beginning of Year 2000. The numbers grow by x during the year. A famine hits his village in the next year and many of his sheep die. The sheep population decreases by y during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheep. Which of the following is correct?

a

x>y

b

y>x

c

x=y

d

cannot be determined

Let us assume the value of x to be 10%

Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10% of 1 million = 1.1 million

In 2001, the numbers decrease by y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.

In terms of the percentage of the number of sheep alive at the beginning of 2001,

it will be (0.1/1.1) ** 100% = 9.09%

From the above illustration it is clear that x>yx

5

X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?

a

14400

b

26400

c

12000

d

12500

Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5

Share of X in the profit = 26400 ** (6/11) = 2400 ** 6 = 14400

6

Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?

a

75000

b

70000

c

72000

d

78000

Ratio of the profits = 25000*12 : 60000*8

= 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2

= 5:8

Let the total profit = x.

Then Kamal received (10x)/100 = x/10 as commission for managing the business

Remaining profit = x- x/10 = (9x)/10 which is shared in the ration 5:8

Kamal's share = x/10 + ((9x)/10) * (5/13) = 58000

=> x + 9x(5/13) = 580000

=> x(1 + 45/13) = 580000

=> x ( 58/13) = 580000

=> x ( 1/13) = 10000

=> x = 130000

Kiran's share = 130000 - 58000 = 72000

7

A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used ?

a

12 months

b

10 months

c

14 months

d

16 months

B received 2/3 of the profit

=> A : B = 1/3 : 2/3 = 1:2

Let the total capital = x

Then A's capital = x/4

B's capital = x – x/4 = (3x)/4

Assume B's money was used for b months

Then A:B = (x/4)**15 : ((3x)/4)**b = 1 : 2

=> 15/4 : (3b)/4 = 1 : 2

=> 15 : 3b = 1 : 2

=> 5 : b = 1 : 2

=> 5/b = 1/ 2

=> b = 5**2 = 10

8

What is 12 percent of 80 percent of 50?

a

5

b

6

c

4.8

d

3.6

12% of 80% of 50

= 12% of (80/100 ** 50)

= 12% of 40

= 12/100 ** 40

= 4.8