Question

A certain sum of money amounts to ₹8700 in 7 years and ₹7500 in 5 years. Find the sum and the rate of simple interest.

Answer 1

Let the sum be P and I be the interest and R be the rate of simple interest
Hence,

Amount in 7 years = ₹ 8700 ➡P + I in 7 years = ₹ 8700.........................(i)
Amount in 5 years = ₹ 7500 ➡P + I in 5 years = ₹ 7500.........................(ii)

Subtracting (ii) from (i),
I in 2 years = ₹ 1200 ➡ Interest in 2 years = ₹ 1200
Now,
Interest in 1 year = ₹(1200/2) = ₹ 600

Interest in 7 years = ₹(600×7) = ₹ 4200
Amount in 7 years = P + Interest in 7 years
➡₹ 8700 = P + ₹ 4200
➡P = ₹(8700-4200) = ₹ 4500

For calculating rate of interest let's consider interest for 1 year.
Now,
R = (I × 100)÷(P × T) = (₹ 600 × 100)÷(₹ 4500 × 1) = ₹ 60000 ÷ ₹ 4500 = ₹ 600 ÷ ₹ 45 = 40/3%

Hence,
$R = 13 \frac{1}{3} \%$

Finally,
$Principal \: = rupees \: 4500 \\ Rate \: of \: simple \: interest = 13 \frac{1}{3} \%$

Hope it helps!