If by selling a table for 540/-, a carpenter loses 4%, for what amount should he sell it, so as to gain 12%?>/p>

Given:

By selling a table at Rs. 540 a carpenter loses 4%.

To do:

We have to find the amount at which he has to sell the table so as to gain 12%.

Solution:

Let the Cost price of the table be $x$.

Loss% $=\frac{Loss}{C.P.} \times 100$

Loss% $=\frac{C.P. - S.P.}{C.P.} \times 100$

$4 = \frac{x-540}{x}\times100$

$ \frac{4}{100}= \frac{x-540}{x}$

$\frac{1}{25} = \frac{x-540}{x}$ 

$x = 25(x - 540)$

$x = 25x - 13500$

$25x - x = 13500$

$24x = 13500$

$x = \frac{13500}{24}$

$x =Rs. 562.50$

The original price of the table$=Rs. 562.50$

To gain 12%, let the gain be Rs. $y$.

Therefore,

$12=\frac{y}{562.5}\times100$

$y=\frac{12\times562.5}{100}$

$y=\frac{6750}{100}$

$y=67.50$

Therefore, the selling price of the table$=Rs. (562.50+67.50)=Rs. 630$.

The table should be sold at Rs. 630, so as to gain 12%.

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Updated on: 10-Oct-2022

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