Question

Mukesh spent 1by6 of his pocket money for buying a birthday gift.he spent 3by5 of the remaining amount for the school canteen. He was still left with ₹100.find:1) his pocket money. 2) amount spent for school canteen

Answer 1

$\textsf{\underline{\large{Given:}}} \\ \hookrightarrow \textsf{Mukesh spent {}^{1} \! {/}_{6} of his pocket money}\\ \textsf{for buying birthday gift.} \\ \\ \hookrightarrow \textsf{He also spent {}^{3} \! {/}_{5} of the remaining}\\ \textsf{amount for the school canteen.}\\ \\ \textsf{\underline{\large{To Find:}}} \\ \hookrightarrow \textsf{Pocket money}\\ \hookrightarrow \textsf{Amount spent for school canteen.}$$\textsf{\underline{\large{Solution:}}} \\ \\ \textsf{Let the amount of his pocket money be x .} \\ \textsf{According to the question,} \\ \Rightarrow \quad \textsf{Amount spent for gift = \dfrac{x}{6} } \qquad \hdots (1) \\ \\ \sf Also, \\ \Rightarrow \quad \textsf{Amount spent at canteen = \dfrac{3}{6} (\sf Remaining\: amount) } \\ \Rightarrow \quad \textsf{ \dfrac{3}{6} \bigg( x - \dfrac{x}{6} \bigg) } \\ \\ \\ \Rightarrow \quad \textsf{ \dfrac{\not{3}^{1}}{6} \times \dfrac{6x - x}{\not{6}_{2}} }$$\therefore \quad \textsf{Amount spent at canteen = \dfrac{5x}{12} } \qquad \hdots (2) \\ \\ \textsf{Now, It is given that after spending on all this} \\ \textsf{Mukesh is left with Rs. 100} \\ \sf So, \\ \\ \Rightarrow \quad \textsf{Money left = Pocket money - money spent} \\ \\ \Rightarrow \quad \textsf{ 100 = x - \bigg( \dfrac{x}{6} + \dfrac{5x}{12} \bigg) \qquad \big[ from (1) \& (2) \big]} \\ \\ \\ \Rightarrow \quad \textsf{ 100 = x - \dfrac{7x}{12} }$$\Rightarrow \quad \textsf{ 1200 = 5x } \\ \\ \therefore \quad \textsf{\bold{Pocket money} = Rs.\:240 } \\ \\ \sf So, \\ \Rightarrow \quad \textsf{Amount spent at school canteen = \dfrac{5x}{12} } \quad \big[ from (2) \big] \\ \\ \Rightarrow \quad \textsf{ \dfrac{5 \times 240}{{12}} } \\ \\ \Rightarrow \quad \textsf{ 5 \times 20 } \\ \\ \Rightarrow \quad \textsf{ 100 } \\ \\ \\ \therefore \quad \textsf{Amount spent at school canteen = Rs. \: 100 }$

Answer 2

Step-by-step explanation:

$\begin{gathered}\textsf{\underline{\large{Given:}}} \\ \\\hookrightarrow\textsf{Mukesh spent {}^{1} \! {/}_{6} of his pocket money}\\ \textsf{for buying birthday gift.} \\ \\ \hookrightarrow \textsf{He also spent {}^{3} \! {/}_{5} of the remaining}\\ \textsf{amount for the school canteen.}\\ \\ \textsf{\underline{\large{To Find:}}} \\ \hookrightarrow \textsf{Pocket money}\\ \hookrightarrow \textsf{Amount spent for school canteen.}\\ \\\end{gathered}$

Let the amount of his pocket money be :

According to the question:

Amount spent for gift :

x/6

Also, Amount spent at canteen:

$\dfrac{3}{6}$

Remaining\amount

$\dfrac{3}{6}$$\bigg( x - \dfrac{x}{6} \bigg)$

$\dfrac{\not{3}^{1}}{6} \times$$\dfrac{6x - x}{\not{6}_{2}}$

Amount spent at canteen = $\dfrac{5x}{12}$

Now, It is given that after spending on all this:

Mukesh is left with Rs. 100}

So,

$100 = x - \bigg( \dfrac{x}{6} + \dfrac{5x}{12} \bigg)$

$\big[ from (1) \& (2) \big]$

${100 = x - \dfrac{7x}{12}}$

So, Amount spent at school canteen = $\dfrac{5x}{12}$

$\big[ from (2) \big]$

$\dfrac{5 \times 240}{{12}}$

${5 \times 20}$

Amount spent at school canteen= Rs. 100.