Question

A sum of money at simple interest amounts to ₹600 in 4 years and ₹625 in 5 years. What is the sum invested?

• A. ₹450
• B. ₹500
• C. ₹525
• D. ₹550

Answer 1

The correct option is B ₹500

We know,
for a principal P, rate of interest R and time T,
Simple Interest = $\frac{P\times R\times T}{100}$

Amount = $P+\frac{P\times R\times T}{100}$

Therefore, amount after 4 years
= $P+\frac{P\times R\times 4}{100}$ = ₹600

amount after 5 years
= $P+\frac{P\times R\times 5}{100}$ = ₹625

Simple interest for 1 year
= Amount after 5 years - Amount after 4 years

= ₹(625 - 600)

= ₹25

$\therefore$$\frac{P\times R\times 1}{100}$ = ₹25

Simple interest for 4 years = $\frac{P\times R\times 4}{100}$ = ₹(25 $\times$ 4) = ₹100

Hence, amount after 4 years
= $P+\frac{P\times R\times 4}{100}$ = ₹600

$\Rightarrow$ P + ₹100 = ₹600

$\Rightarrow$ P = ₹600 - ₹100

$\Rightarrow$ P = ₹500