Question

Rahul, Reena and Ruhi want to divide $₹1072$ amongst themselves in the ratio of $\frac{1}{4}:\frac{2}{3}:\frac{1}{5}$ respectively. Find the share of each of them.

Answer 1

Let the amount of money received by Rahul, Reena and Ruhi be $\frac{1}{4}x$, $\frac{2}{3}x$ and $\frac{1}{5}x$.

Step 1: Find the value of $x$

The total amount of money $=₹1072$

$\Rightarrow$ $\frac{x}{4}+\frac{2x}{3}+\frac{x}{5}=1072$

$\Rightarrow$ $\frac{15x}{60}+\frac{40x}{60}+\frac{12x}{60}=1072$ ( converting the fractions into like fractions by taking L.C.M of the denominators )

$\Rightarrow$ $\frac{15x+40x+12x}{60}=1072$

$\Rightarrow$ $\frac{67x}{60}=1072$

$\Rightarrow$ $67x=1072\times 60$

$\Rightarrow$ $x=\frac{1072\times 60}{67}$

$\Rightarrow$ $x=960$

Step 2: Find the value of $\frac{1}{4}x$, $\frac{2}{3}x$ and $\frac{1}{5}x$

If $x=960$, $\frac{x}{4}=\frac{960}{4}$

$\Rightarrow$ $\frac{x}{4}=240$

Similarly, $\frac{2x}{3}=\frac{2\times 960}{3}$

$\Rightarrow$ $\frac{2x}{3}=640$

Also, $\frac{x}{5}=\frac{960}{5}$

$\Rightarrow$ $\frac{x}{5}=192$

Hence, Rahul's share is $₹240$, Reena's share is $₹640$ and Ruhi's share is $₹192$.