On selling a tea-set at 5% loss and a lemon-set at 15% gain, a shopkee

1.	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.
Answer» 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.

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.

Answer»

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.