Simple interest on a certain sum is one-fifth of the sum and the interest rate per cent per annum is 5 times the number of years. If the rate of interest increases by 3%, then how much will the simple interest (in ₹) be on ₹5,600 for 6 years?

Question

Accepted Answer

Let the principal be P, rate per annum be R%, and time be T years.

Given: Simple interest (SI) is one-fifth of the sum (P).
So, SI = P/5.

We know SI = (P × R × T)/100.
So, (P × R × T)/100 = P/5
=> R × T = 100/5 = 20
=> R × T = 20

Also, rate per cent per annum is 5 times the number of years:
R = 5T

Substitute R in R × T = 20:
(5T) × T = 20
=> 5T^2 = 20
=> T^2 = 4
=> T = 2 (since time cannot be negative)

So, T = 2 years, R = 5T = 10%

Now, the question asks: If the rate increases by 3%, what will be the SI on ₹5,600 for 6 years?

New rate = 10% + 3% = 13%
Time = 6 years
Principal = ₹5,600

SI = (P × R × T)/100 = (5600 × 13 × 6)/100
First, 13 × 6 = 78
So, SI = (5600 × 78)/100 = (5600 × 78) ÷ 100

Calculate 5600 × 78:
5600 × 78 = (5600 × 80) - (5600 × 2) = (448,000) - (11,200) = 436,800

Now, divide by 100:
436,800 ÷ 100 = 4,368

Therefore, the simple interest is ₹4,368.

Correct answer: ₹4,368

Answer

Answer

Answer