Question

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.

Answer 1

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

ATP, $\frac{15}{100}\times y-\frac{5}{100}\times x=70\Rightarrow 3y-x=70\times 20\Rightarrow 3y-x=1400⟶\left(1\right)$

Again,

$\frac{5}{100}\times x+\frac{10}{100}\times y=130\Rightarrow x+2y=130\times 20\Rightarrow x+2y=2600⟶\left(2\right)$

Substituting $x$ from equation $\left(1\right)$ in equation $\left(2\right)$

$3y-1400+2y=2600\Rightarrow 5y=4000\Rightarrow y=800$