Question

A sum of money amounts to Rs.12322.8 after 7 years and Rs.15724.8 after 12 years at the same rate. What is the rate of interest per annum (simple interest)?
1. 12.5%
2. 15%
3. 9%
4. 6%
5. 10%

Answer 1

Correct Answer - Option 3 : 9%

Given:

Amount (A₁) = Rs. 12322.8

Amount (A₂) = Rs. 15724.8

Time (T₁) = 7 years

Time (T₂) = 12 years

Concept Used:

SI = PRT/100

P = Principal, R = Rate of Interest and T = Time.

Calculation:

Difference in time = 12 - 7

⇒ 5 years

According to the question, we get

SI in 5 years = A₂ - A₁

⇒ SI in 5 years = 15724.8 - 12322.8

⇒ SI in 5 years = Rs. 3402

SI in 1 year = Rs. 3402 ÷ 5

⇒ SI in 1 year = Rs. 680.4

SI in 7 years = Rs. 680.4 × 7

⇒ SI in 7 years = Rs. 4762.8 

Principal (P) = Rs.12322.8 – Rs.4762.8 = Rs.7560

we have,

SI = PRT/100

⇒ 4762.8 = (7560 × 7R)/100

⇒ R = 9%

∴ The rate of interest of simple interest is 9%.