English

On Selling a Tea-set at 5% Loss and a Lemon-set at 15% Gain, a Shopkeeper Gains Rs. 7. However, If He Sells the Tea-set at 5% Gain and the Lemon-set at 10% Gain, He Gains Rs. 14.

Question

On selling a tea-set at 5% loss and a lemon-set at 15% gain, a shopkeeper gains Rs. 7. However, if he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains Rs. 14. Find the price of the tea-set and that of the lemon-set paid by the shopkeeper.

Solution

Let the actual price of the tea and lemon set be Rs.x and Rs.y respectively.
When gain is Rs.7, then
`y/100 × 15 - x/100 × 5 = 7`
⇒ 3y – x = 140 ……..(i)
When gain is Rs.14, then
`y/100 × 5 + x/100 × 10 = 14`
⇒ y + 2x = 280 ……..(ii)
Multiplying (i) by 2 and adding with (ii), we have
7y = 280 + 280
`⇒ y = 560/7 = 80`
Putting y = 80 in (ii), we get
80 + 2x = 280
`⇒ x = 200/2 = 100`
Hence, actual price of the tea set and lemon set are Rs.100 and Rs.80 respectively.