Question

A sum of money at simple interest amounts to ₹854 in 4 years and to ₹893 in 5 years. What is the sum invested?

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

Answer 1

The correct option is A ₹698

Given that, a sum of money at simple interest amounts to ₹854 in 4 years and to ₹893 in 5 years.
Let principal = P, rate of interest = R and time = T,
As we know,
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 5 years
= $P+\frac{P\times R\times 5}{100}$ = ₹893

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

$\Rightarrow$ $\frac{P\times R\times 1}{100}$= ₹(893 - 854)
$\Rightarrow$ $\frac{P\times R}{100}$= ₹39 ...(i)

$\therefore$ Simple interest for 4 years = $\frac{P\times R\times 4}{100}$ $=39\times 4=₹156$ [from equation (i)]

Hence, amount after 4 years
= $P+\frac{P\times R\times 4}{100}$ = ₹854

$\Rightarrow$ P + ₹156 = ₹854

$\Rightarrow$ P = ₹854 - ₹156

$\Rightarrow$ P = ₹698