On selling a $T . V .$ at $5 %$ gain and fridge at $10 %$ gain, a shopkeeper gains $R s . 2000$ . But if he sells the $T . V .$ at $10 %$ gain and the fridge at $5 %$ loss. He gains $R s . 1500$ on the transaction. Find the actual prices of $T . V .$ and fridge.

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Solution

Let, the price of a TV be $R s . x$ and that of a fridge be $R s . y$

Then, we have:

$\frac{5 x}{100} + \frac{10 y}{100} = 2000$

$5 x + 10 y = 200000$

$\Rightarrow x + 2 y = 40000$

$\Rightarrow x = 40000 - 2 y$ ....(i)

Now,

$\frac{10 x}{100} - \frac{5 y}{100} = 1500$

$\Rightarrow 10 x - 5 y = 150000$

$\Rightarrow 2 x - y = 30000$

$\Rightarrow 2 (40000 - 2 y) - y = 30000$ from euation (i)

$\Rightarrow 80000 - 4 y - y = 30000$

$\Rightarrow 5 y = 80000 - 30000$

$\Rightarrow y = \frac{50000}{5}$

$\Rightarrow y = R s 10000$

$∴ x = R s 40000 - R s 20000$

$\Rightarrow x = R s .20000$

$∴$ Price of a T.V. $= R s . 20000$

Price of a fridge $= R s 10000$

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