Question

Divide Rs. $1586$ in three parts such a way that their amounts at the end of $2,3$ and $4$ years at $5\%$ per annum simple interest be equal.

• A. Rs. $732$, Rs. $488$, Rs. $366$
• B. Rs. $560$, Rs. $520$, Rs. $506$
• C. Rs. $556$, Rs, $524$, Rs. $506$
• D. Rs. $548$, Rs. $528$, Rs. $510$

Answer 1

The correct option is A Rs. $732$, Rs. $488$, Rs. $366$

The ratio in which the sum was divided $=\frac{1}{r_1{t}_1}:\frac{1}{r_2{t}_2}:\frac{1}{r_3{t}_3}$

$=\frac{1}{5\times 2}:\frac{1}{5\times 3}:\frac{1}{5\times 4}$

$=\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

$=6:4:3$

Hence, $1st$ part $=$ Rs. $\frac{6}{13}\times 1586=$ Rs. $732$

$2^{nd}$ part $=$ Rs. $\frac{4}{13}\times 1586=$ Rs. $488$

$3^{rd}$ part $=$ Rs. $\frac{3}{13}\times 1586=$ Rs. $366$

Hence, option A is correct.