Question

Question 121
Huma, Hubna and Seema received a total of Rs . 2016 as monthly allowance from their mother such that Seema gets $\frac{1}{2}$ of what Hubna gets and Huma gets $1\frac{2}{3}$ times Seema's share. How much money do the three sisters get individually?

Answer 1

Seema gets allowance
$=\frac{1}{2}$ of Hubna's share

Huma gets allowance
$=1\frac{2}{3}$ of Seema's share
$=\frac{5}{3}$ of Seema's share
$=\frac{5}{3}$ of $\frac{1}{2}$ of Hubna's share
[$\because$ Seema's share $=\frac{1}{2}$ of Hubna's share]
$=\frac{5}{3}\times \frac{1}{2}$ of Huma's share
$=\frac{5}{6}$ of Hubna's share

But Huma, Hubna and Seema received total monthly allowance from their mother = ₹ 2016

$\therefore$ Huma's share + Hubna's share + Seema's share = ₹ 2016

1 of Hubna's share + $\frac{5}{6}$ of Hubna's share + $\frac{1}{2}$ of Hubna's share = ₹ 2016

So, $(1+\frac{5}{6}+\frac{1}{2})$ of Hubna's share = ₹ 2016

$\Rightarrow \left(\frac{6+5+3}{6}\right)$ of Hubna's share = ₹ 2016
$\Rightarrow \frac{14}{6}$ of Hubna's share = ₹ 2016

$\therefore$ Hubna's share
$=₹2016÷\frac{14}{6}$

$=₹2016\times \frac{6}{14}=144\times 6=₹864$

So, Seema's share $=\frac{1}{2}$ of 864 $=\frac{1}{2}\times 864=₹432$

and Huma's share $=\frac{5}{6}$ of 864 $=\frac{5}{6}\times 864=5\times 144=₹720$

Hence, Huma, Hubna and Seema get ₹ 720, ₹ 864 and ₹ 432, respectively.