Question

Divide Rs. $2379$ into $3$ parts, so that their amounts after $2,3$ and $4$ years respectively may be equal the rate of interest being $5\%$ per annum at simple interest. The first part is

• A. Rs. $759$
• B. Rs. $792$
• C. Rs. $818$
• D. Rs. $828$

Answer 1

Answer: (D)

Rs. $828$

Let the three parts be $x,y$ and $z$.

Then, $x+$ $\frac{x\times 2\times 5}{100}=y+\frac{y\times 3\times 5}{100}=z+\frac{z\times 4\times 5}{100}$
$\Rightarrow x+\frac{x}{10}=y+\frac{3y}{20}=z+\frac{z}{5}$
$\frac{11x}{10}=\frac{23y}{20}=\frac{6z}{5}=k\left(say\right)$
$\therefore x=\frac{10k}{11},y=\frac{20k}{23},z=\frac{5k}{6}$
Given, $x+y+z=2379$
$\Rightarrow \frac{10k}{11}+\frac{20k}{23}+\frac{5k}{6}=2379$
$\Rightarrow \frac{1380k+1320k+1265k}{1518}=2379$
$\Rightarrow 3965k=2379\times 1518$
$\Rightarrow k=\frac{2379\times 1518}{3965}$
$\Rightarrow$ First part $=$ Rs. $\frac{10\times 3\times 1518}{11\times 5}=$ Rs. $828$