Question

A sum lent at the simple interest at the rate of 5% per annum for 4 years, amounts to ₹ 6,000. What is the ratio of the sum to the interest earned in five years?

• A. 1 : 4
• B. 2 : 4
• C. 4 : 3
• D. 4 : 1

Answer 1

The correct option is D 4 : 1

Amount = ₹ 6,000
Rate of interest = 5%
Time period = 4 years

Let the principal be P.

$\text{We know that simple interest,}\text{S.I =}\frac{P\times R\times T}{100}\text{and Amount - Principal = Interest}$

$\therefore 6,000-P=\frac{P\times 5\times 4}{100}$

$\Rightarrow 6,000-P=\frac{P}{5}$

$\Rightarrow P=6,000\times 5-5P$
$\Rightarrow 6P=6,000\times 5$
$\Rightarrow P=₹5,000$

$\text{Interest after 5 years,}\text{S.I =}\frac{5,000\times 5\times 5}{100}$

$\Rightarrow \text{S.I =}₹1,250$

So, the ratio of its principal to the interest after five years is

$\frac{P}{S.I}=\frac{₹5,000}{₹1,250}$

$\Rightarrow \frac{P}{S.I}=\frac{4}{1}$

$\text{Hence,}\text{principal (P) : simple interest (S.I)}=4:1$