Question

Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years she received Rs. 210 as compound interest, but paid Rs. 200 only as simple interest. Find the sum and the rate of interest.

Answer 1

Given details are,

C.I that Kamala receives = Rs 210

S.I that Kamala paid = Rs 200

Time = 2 years

So,

We know, SI = PTR/100

= P×2×R/100

P×R = 10000 ………….. Equation 1

CI = A – P

CI = P [(1 + R/100)ⁿ – 1]

210 = P [(1 + R/100)² – 1]

210 = P (1² + R²/100² + 2(1)(R/100) – 1) (by using the formula (a+b)²)

210 = P (1 + R²/10000 + R/50 – 1)

210 = P (R²/10000 + R/50)

210 = PR²/10000 + PR/50

We know PR = 10000 from Equation 1

210 = 10000R/10000 + 10000/50

210 = R + 200

R = 210 – 200

= 10%

In Equation 1, PR = 10000

P = 10000/R

= 10000/10

= 1000

∴ Required sum is Rs 1000.