BENCHHMARK

Questions :

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

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 %.