## Aptitude Solved Problems

Questions :

1. The ratio between the present ages of Arun and Aravind is 6 : 7. If Aravind is 4 years old than Arun, what will be the ratio of the ages of Arun and Aravind after 4 years ?

2. The volume of a cube is 729 cm3 . Find the surface area of a cube?

3. The sum of three numbers is 123. If the ratio between first and second numbers is 2:5 and that of between second and third is 3:4, then find the difference between second and the third number ?

4. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. What is the rate of interest per annum ?

Answers :

1. 7 : 8.

2. 486 cm2.

3. 15.

4. 12 %.

1. Explanation:

Let Arun age and Aravind age is 6x years and 7x years.

7x – 6x = 4

x = 4

Required ratio = ( 6x + 4 ) : ( 7x + 4 )

= [ ( 6 * 4 ) + 4 ] : [ ( 7 * 4 ) + 4 ]

= ( 24 + 4 ) : ( 28 + 4 )

= 28 : 32

= 7 : 8

∴ The ratio of the ages will be 7 : 8.

2. Explanation:

Volume of a cube = a 3 cm3

729 cm3 = a3 cm3

a3 cm3 = 93 cm3

Taking cube root on both sides

a = 9 cm

The surface area of a cube = 6 a2 cm2

= 6 * ( 92) cm2

= ( 6 * 81 ) cm2

= 486 cm2

∴ The surface area of a cube is 486 cm2.

3. Explanation:

a : b = 2 : 5 and b : c = 3 : 4

So, a : b : c = 6 : 15 : 20

( 2 * 3 = 6 ), ( 5 * 3 = 15) or ( 3 * 5 = 15), ( 5 * 4 = 20 )

Total Ratio = 6 + 15 + 20

Total Ratio = 41

41x = 123

x = ( 123 / 41 )

x = 3

Difference between second and the third number = 20x – 15x

= 5x

= ( 5 * 3 )

= 15

∴ The difference between second and the third number is 15.

4. Explanation:

Simple interest for 3 years = Simple interest for 8 years – 5 years

Simple interest for 3 years = ( 12005 – 9800 )

Simple interest for 3 years = 2205

Simple interest for 1 year = ( 2205 / 3 )

Simple interest for 5 years = ( 2205 / 3 ) * 5

= ( 735 * 5 )

= Rs. 3675

Principal = ( 9800 – 3675 ) = 6125

Rate = ( 100 * Simple Interest ) / ( Principal * Time )

Rate = ( 100 * 3675 ) / ( 6125 * 5 )

= ( 20 * 3675 ) / 6125

= ( 73500 / 6125 )

= 12 %

∴ Rate of interest per annum is 12 %.