Abhishek sold an umbrella to Gaurav at a gain of 20% and gaurav sold the same umbrella to Mukhal at a loss of 10%. If Mukhul paid rs 1080 for it , then how much did Abhishek pay for it.

Dear Student,

Please find below the solution to the asked query:

Let , Abhishek pays for umbrella = x  , So

Given : Abhishek sold an umbrella to Gaurav at a gain of 20%  , So

Gaurav pays for umbrella  = x  + 20 % of x  =  x  + $\frac{20 x}{100} = x + \frac{x}{5} = \frac{\mathbf{6}\mathit{ }\mathit{x}}{\mathbf{5}}$

Also given : Gaurav sold the same umbrella to Mukhal at a loss of 10% , So

Mukhal pays for umbrella  = $\frac{6 x}{5}$  - 10 % of $\frac{6 x}{5}$  =  $\frac{6 x}{5}$  + $\frac{10 \times {\displaystyle \frac{6 x}{5}}}{100} = \frac{6 x}{5} - \frac{2 \times {\displaystyle 6 x}}{100} = \frac{6 x}{5} - \frac{3 x}{25} = \frac{30 x - 3 x}{25}= \frac{\mathbf{27}\mathbf{ }\mathit{x}}{\mathbf{25}}$

But given : Mukhul paid Rs 1080 for umbrella  , So

$$\begin{gathered} \frac{27 x}{25} = 1080 \\ \Rightarrow x = 1080 \times \frac{25}{27} \\ \Rightarrow x = 40 \times 25 \\ \mathbf{\Rightarrow }\mathbf{ }\mathit{x}\mathbf{ }\mathbf{=}\mathbf{1000} \end{gathered}$$
Therefore,

Abhishek pays for umbrella = Rs . 1000                                                     ( Ans )

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