Plzzz help in this

Plzzz help in this Narinder spends 60% of his income on household expenses,' 20% of the remainder on recraafiöh and 200/0@Che Femainder on petrol. Whateverhsléftis his sayingUhe "saves 2560 per month, what is his income?

Dear Student,

Please find below the solution to the asked query:

Let , Income of Narinder = x , So

Amount he spends on household expenses = 60 % of x  = $\frac{60 x}{100} = \frac{{\displaystyle \mathbf{3}\mathbf{ }\mathbf{x}}}{{\displaystyle \mathbf{5}}}$ , So

Amount left after he spend money on household expenses = x - $\frac{3 x}{5} = \frac{{\displaystyle 5 x - 3 x}}{{\displaystyle 5}} = \frac{\mathbf{2}\mathbf{ }\mathbf{x}}{\mathbf{5}}$
Then, from given condition :

Amount he spends on recreation = 20 % $\frac{{\displaystyle 2 x}}{{\displaystyle 5}} = \frac{20 \times {\displaystyle \frac{2 x}{5}}}{100}= \frac{{\displaystyle \frac{2 x}{5}}}{5} = \frac{\mathbf{2}\mathbf{ }\mathbf{x}}{\mathbf{25}}$ , So

Amount left after he spend money on household expenses and  on recreation =  $\frac{2 x}{5} - \frac{2 x}{25} = \frac{10 x - 2 x}{25} = \frac{\mathbf{8}\mathbf{ }\mathbf{x}}{\mathbf{25}}$

Then, from given condition :

Amount he spends on petrol = 20 % $\frac{{\displaystyle 8 x}}{{\displaystyle 25}} = \frac{20 \times {\displaystyle \frac{8 x}{25}}}{100}= \frac{{\displaystyle \frac{8 x}{25}}}{5} = \frac{\mathbf{8}\mathbf{ }\mathbf{x}}{\mathbf{125}}$ , So

Amount left after he spend money on household expenses and  on recreation and on petrol = $\frac{8 x}{25} - \frac{8 x}{125} = \frac{40 x - 8 x}{125} = \frac{\mathbf{32}\mathbf{ }\mathbf{x}}{\mathbf{125}}$

Also given : Whatever is left is his saving and he saves Rs. 2560 per month , So

$$\begin{gathered} \frac{32 x}{125} = 2560 \\ \Rightarrow x = 2560 \times \frac{125}{32} \\ \Rightarrow x = 80 \times 125 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{ }\mathbf{=}\mathbf{10000} \end{gathered}$$

Therefore,

Income of Narinder = Rs.. 10000                                               ( Ans )


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