Question

Huma, Hubna and Seema received a total of $₹2,016$ as a monthly allowance from their mother such that Seema gets $\frac{1}{2}$ of what Huma gets and Hubna gets $1\frac{2}{3}$ times Seema’s share.

How much money do the three sisters get individually?

Answer 1

Step 1: Assume variable and calculate shares

Let, Huma's share $=₹x$

Then, Seema's share $=\frac{1}{2}$ of Huma's share

$=₹\left(\frac{1}{2}ofx\right)$

$=₹\left(\frac{1}{2}\times x\right)$ [using BODMAS]

$=₹\frac{1}{2}x$

And, Hubna's share $=1\frac{2}{3}$ of Seema's share

$=₹\left(1\frac{2}{3}of\frac{1}{2}x\right)$

$=₹\left[\frac{\left(1\times 3\right)+2}{3}of\frac{1}{2}x\right]$ $\left[\because a\frac{b}{c}=\frac{\left(a\times c\right)+b}{c}\right]$

$=₹\left[\frac{5}{3}of\frac{1}{2}x\right]$

$=₹\left[\frac{5}{3}\times \frac{1}{2}x\right]$ [using BODMAS]

$=₹\left[\frac{5\times 1}{3\times 2}x\right]$

$=₹\frac{5}{6}x$

Step 2: Form an equation and simplify it for $x$

According to the question, the total monthly allowance received is $₹2,016$.

i.e., Huma's share $+$ Seema's share $+$ Hubna's share $=₹2,016$

$\Rightarrow$ $x+\frac{1}{2}x+\frac{5}{6}x=2016$

$\frac{6x+3x+5x}{6}=2016$

$\frac{14x}{6}=2016$

$x=2016\times \frac{6}{14}$

$x=144\times \frac{6}{1}$

$x=864$

Step 3: Find each person's share

So, Huma's share $=₹x$

$=₹864$

And, Seema's share $=₹\frac{1}{2}x$

$=₹\frac{1}{2}\times 864$

$=₹432$

Also, Hubna's share $=₹\frac{5}{6}x$

$=₹\frac{5}{6}\times 864$

$=₹\frac{5}{1}\times 144$

$=₹720$

Hence, the shares of the three sisters Huma, Seema and Hubna are $₹864,₹432$ and $₹720$ respectively.