On selling a tea set at $5 %$ loss and a lemon set at $15 %$ gain, a shopkeeper gains Rs. $70$ . If he sells the tea set at $5 %$ gain and lemon set at $10 %$ gain, he gains Rs. $130$ . Find the cost price of the lemon set.

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Solution

Let $C . P$ of tea set $= x$ and lemon set $= y$
ATP, $\frac{15}{100} \times y - \frac{5}{100} \times x = 70 \Rightarrow 3 y - x = 70 \times 20 \Rightarrow 3 y - x = 1400 ⟶ (1)$
Again,
$\frac{5}{100} \times x + \frac{10}{100} \times y = 130 \Rightarrow x + 2 y = 130 \times 20 \Rightarrow x + 2 y = 2600 ⟶ (2)$
Substituting $x$ from equation $(1)$ in equation $(2)$
$3 y - 1400 + 2 y = 2600 \Rightarrow 5 y = 4000 \Rightarrow y = 800$

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On selling a tea set at 5% loss and a lemon set at 15% gain, a shopkeeper gains Rs. 70. If he sells the tea set at 5% gain and lemon set at 10% gain, he gains Rs. 130. Find the cost price of the lemon set.

Let C.P of tea set =x and lemon set =yATP, 15100×y−5100×x=70⇒3y−x=70×20⇒3y−x=1400⟶(1)Again,5100×x+10100×y=130⇒x+2y=130×20⇒x+2y=2600⟶(2)Substituting x from equation (1) in equation (2)3y−1400+2y=2600⇒5y=4000⇒y=800

On selling a tea set at $5 %$ loss and a lemon set at $15 %$ gain, a shopkeeper gains Rs. $70$ . If he sells the tea set at $5 %$ gain and lemon set at $10 %$ gain, he gains Rs. $130$ . Find the cost price of the lemon set.