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

Let C.P. of tea set = ₹x and C.P. of lemon set = ₹y.

Given, Loss on tea set = 5% and gain on lemon set = 15%, total gain = ₹70.

$\therefore \dfrac{15}{100}y - \dfrac{5}{100}x = 70 \\[1em] \Rightarrow \dfrac{15y - 5x}{100} = 70 \\[1em] \Rightarrow 15y - 5x = 7000 \\[1em] \Rightarrow 3y - x = 1400 ……(i)$

Given, Gain on tea set = 5% and gain on lemon set = 10%, total gain = ₹130.

$\therefore \dfrac{5}{100}x + \dfrac{10}{100}y = 130 \\[1em] \Rightarrow \dfrac{5x + 10y}{100} = 130 \\[1em] \Rightarrow 5x + 10y = 13000 \\[1em] \Rightarrow x + 2y = 2600 ……(ii)$

Adding eq. (i) and (ii) we get,

⇒ (3y - x) + (x + 2y) = 1400 + 2600

⇒ 5y = 4000

⇒ y = 800.

Hence, C.P. of lemon set = ₹800.