On selling a tea-set at $5 %$ loss and a lemon-set at $15 %$ gain, a crockery seller gains Rs $7$ . If he sells the tea-set at $5 %$ gain and the lemon-set at $10 %$ gain, he gains Rs $13$ . Find the actual price of the tea-set and the lemon-set.

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Solution

Let the cost price of the tea-set and the lemon-set be Rs x and Rs y respectively.

$C a s e I$ : When tea set is sold at $5 %$ loss and lemon-set at $15 %$ gain.

Loss in tea-set $=$ Rs. $\frac{5 x}{100} =$ Rs. $\frac{x}{20}$

Gain on lemon-set $=$ Rs. $\frac{15 y}{100} =$ Rs. $\frac{3 y}{20}$

$∴$ Net gain $=$ Rs. $\frac{3 y}{20} - \frac{x}{20}$

$\Rightarrow \frac{3 y}{20} - \frac{x}{20} = 7$

$\Rightarrow 3 y - x = 140$

$\Rightarrow x - 3 y + 140 = 0$ (i)

$C a s e I I$ : When tea-set is sold at $5 %$ gain and the lemon-set at $10 %$ gain.

Gain on tea-set $=$ Rs. $\frac{5 x}{100} =$ Rs. $\frac{x}{20}$

Gain on lemon-set $=$ Rs. $\frac{10 y}{100} =$ Rs. $\frac{y}{100}$

$∴$ Total gain $=$ Rs. $\frac{x}{20} + \frac{y}{10}$

$\Rightarrow \frac{x}{20} + \frac{y}{10} = 13$

$\Rightarrow x + 2 y = 260$

$\Rightarrow x + 2 y - 260 = 0$ .(ii)

Subtracting equation (ii) from equation (i), we get
$- 5 y + 400 = 0 \Rightarrow y = 80$

Putting $y = 80$ in equation (i), we get
$x - 240 + 140 = 0 \Rightarrow x = 100$

Hence, the cost prices of tea-set and lemon-set are Rs. $100$ and Rs. $80$ respectively.

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On selling a tea-set at 5% loss and a lemon-set at 15% gain, a crockery seller gains Rs 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains Rs 13. Find the actual price of the tea-set and the lemon-set.

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