Question

A certain sum of money amounts to rs1125 in 5 years and to rs1200 in 8 years. Find the sum and the rate of interest.

Answer 1

Answer:

Sum is Rs 1000 and rate of interest is 2.5%

Explanation:

Formula for Simple Interest is

SI = (P × R × T)/100

where, P = Principal amount, R = Rate of interest, T = Time in years

Concept:

If amount P in specific time T1 amounts to A1 and the same amount P in  time T1 amounts to A2, keeping the rate of interest same, then principal and rate is calculated as

P = (A2T1 - A1T2)/(T1 - T2)

R = (A1 - A2)/(A2T1 - A1T2) × 100

Given that certain sum of money amounts to Rs 1125 in 5 years and to Rs 1200 in 8 years.

We have

A1 = Rs 1125

A2 = Rs 1200

T1 = 5 years

T2 = 8 years

Let the certain sum of money be P and rate of interest be R

Using the above concept

Principal is calculated as

P = (A2T1 - A1T2)/(T1 - T2)

P = [(1200 × 5) - (1125 × 8)]/(5 - 8)

P = (6000 - 9000)/(-3)

P = -3000/-3

P = Rs 1000

Rate of interest is calculated

R = (A1 - A2)/(A2T1 - A1T2) × 100

R = (1125 - 1200)/[(1200 × 5) - (1125 × 8)] × 100

R = [-75/(6000 - 9000)] × 100

R = [-75/-3000] × 100

R = -7500/-3000

R = 75/30

R = 2.5%