Question

A certain sum earns a compound interest of Rs. 1010 for 2 years and the simple interest on the same sum for the same period and the same rate is Rs.1000. Find the sum and the rate of interest.
1. Rs.1700 ; 5%
2. Rs. 1500 ; 2%
3. Rs.2500 ; 2%
4. Rs.1500 ; 5%

Answer 1

Correct Answer - Option 3 : Rs.2500 ; 2%

Given ∶ 

C.I = Rs.1010

S.I = Rs. 1000

T = 2 years

Formula Used∶

R = (SI × 100)/(P × T)

P = (S.I × 100)/(R × T)

and concept of Unitary Method.

Calculation ∶

S.I for 2 years = Rs 1000

S.I for 1 years = Rs.1000/2 = Rs.500

C.I for 1 year = Rs.500      (∵ for first year, C.I = S.I)

Given, C.I for 2 years = Rs.1010

So, C.I for 2nd year = 1010 - 500 = Rs.510

Now, Difference of interests = 510 - 500 = Rs.10

So, Rs.10 is the interest on Rs.500 for one year

Rate of Interest = (10 × 100) / (500 × 1) = 2%

Principal = (500 × 100) / (2 × 1) = Rs. 2500.