Question

A sum of money at simple interest amounts to ₹815 in 3 years and to ₹854 in 4 years. What is the sum invested?

• A. ₹698
• B. ₹700
• C. ₹650
• D. ₹715

Answer 1

The correct option is A

₹698

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
= $P+\frac{P\times R\times 4}{100}$ = ₹854

amount after 3 years
= $P+\frac{P\times R\times 3}{100}$ = ₹815

Simple interest for 1 year
= Amount after 4 years - Amount after 3 years

= $\frac{P\times R\times 1}{100}$

= ₹(854 - 815)

= ₹39

$\therefore$$\frac{P\times R\times 1}{100}$ = ₹39

Simple interest for 3 years = $\frac{P\times R\times 3}{100}$ = ₹ (39 $\times$ 3) = ₹117

Hence, amount after 3 years
= $P+\frac{P\times R\times 3}{100}$ = ₹815

$\Rightarrow$ Principal, P + ₹ 117 = ₹815

$\Rightarrow$ P = ₹815 - ₹117

$\Rightarrow$ P = ₹698