BENCHHMARK

Aptitude Solved Problems
Questions :

1. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?

2. Priya is able to do a piece of work in 15 days and Raja can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

3. There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?

Answers :

1. 54.68.

2. ( 8 / 15 )

3. Rs. 4634.

1. Explanation:

Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1 = ( 55 * 50 )
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2 = ( 60 * 55 )
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3 = ( 45 * 60 )
Total students = ( 55 + 60 + 45 ) = 160
Average mark of all students = [ ( 55 * 50 ) + ( 60 * 55 ) + (45 * 60 ) ] / ( 160 )
= ( 275 + 330 + 270 ) / 16
= ( 875 / 16 )
= 54.68

∴ Average marks of all the students is 54.68.

2. Explanation:

Amount of work Priya can do in 1 day = ( 1 / 15 )
Amount of work Raja can do in 1 day = ( 1 / 20 )
Amount of work Priya and Raja can do in 1 day = ( 1 / 15 ) + ( 1 / 20 ) = 7/60
Amount of work Priya and Raja can together do in 4 days = 4 * ( 7 / 60) = ( 7 / 15 )
Fraction of work left = 1 – ( 7 / 15 )
= ( 8 / 15 )

∴ The fraction of work left is ( 8 / 15 ).

3. Explanation:

Let Principle = Rs. 100
Simple Interest = Rs. 80
Rate of interest= ( 100 * Simple Interest ) / Principle * Time
= ( 100 * 80 ) / ( 100 * 8 )
= 10% per annum
Now let′s find out the compound interest of Rs. 14,000 after 3 years at 10%
Principle = Rs. 14000
Time = 3 years
Rate of Interest = 10%
Amount after 3 years = P ( 1 +( R / 100 ) )T
= 14000 ( 1 + ( 10 / 100 )3 = 14000 ( 110 / 100 )3
= 14000 ( 11 / 10 )3
= 14 (11)3
= 18634
Compound Interest = Rs. 18634 – Rs. 14000
= Rs. 4634

∴ Compound Interest is Rs. 4634.