Question

Manavi and Kuber each receives an equal allowance. The table shows the fraction of their allowance each deposits into his/her saving account and the fraction each spends at the mall. If allowance of each is $₹1260$ find the amount left with each.

Where money goes	Fraction of Allowance for Manavi	Fraction of Allowance for Kuber
Saving Account	$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$	$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$
Spend at mall	$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$	$\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$
Left over	?	?

Answer 1

Step 1: Find leftover money for Manavi.

Given that: Total allowance of Manavi and Kuber each is $₹1260.$

Let the total fraction be $1$.

$\begin{array}{rcl}\mathrm{Left}\mathrm{over}\mathrm{fraction}& =& \mathrm{Total}-\mathrm{fraction}\mathrm{of}\mathrm{spendings}-\mathrm{fraction}\mathrm{of}\mathrm{savings}\\ & =& 1-\left(\frac{1}{2}+\frac{1}{4}\right)\\ & =& 1-\frac{3}{4}\\ & =& \frac{4-3}{4}\\ & =& \frac{1}{4}\end{array}$

$\mathrm{Total}\mathrm{Amount}\mathrm{left}=\mathrm{Left}\mathrm{over}\mathrm{fraction}\times \mathrm{total}\mathrm{allowance}$

$$\begin{gathered} =\frac{1}{4}\times 1260 \\ =\mathrm{Rs}315 \end{gathered}$$

Step 2: Find leftover money for Kuber.

Let the total fraction be $1$.

$\begin{array}{rcl}\mathrm{Left}\mathrm{over}\mathrm{fraction}& =& \mathrm{Total}-\mathrm{fraction}\mathrm{of}\mathrm{spendings}-\mathrm{fraction}\mathrm{of}\mathrm{savings}\\ & =& 1-\left(\frac{1}{3}+\frac{3}{5}\right)\\ & =& 1-\frac{14}{15}\\ & =& \frac{15-14}{15}\\ & =& \frac{1}{15}\end{array}$

$\mathrm{Total}\mathrm{Amount}\mathrm{left}=\mathrm{Left}\mathrm{over}\mathrm{fraction}\times \mathrm{total}\mathrm{allowance}$

$$\begin{gathered} =\frac{1}{15}\times 1260 \\ =\mathrm{Rs}84 \end{gathered}$$

Hence the amount left with Manavi is $\mathrm{Rs}315$ and the amount left with Kuber is $\mathrm{Rs}84.$