Question

On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gains ₹ 7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains ₹ 13. Find the actual price of each of the tea set and the lemon set.

Answer 1

Given: Let the cost price of the tea-set = ₹ x and the lemon-set = ₹ y.

When tea is sold at 5% loss and lemon at 15% gain, net gain = ₹ 7.

When tea is sold at 5% gain and lemon at 10% gain, net gain = ₹ 13.

Step-wise calculation:

1. Case I (5% loss on tea, 15% gain on lemon):

Loss on tea = 5% of x = `x/20`.

Gain on lemon = 15% of y = `(3y)/20`. 

Net gain = `(3y)/20 - x/20 = 7` 

⇒ 3y – x = 140   ...(Equation 1)

2. Case II (5% gain on tea, 10% gain on lemon):

Gain on tea = `x/20`.

Gain on lemon = `y/10`.

Total gain = `x/20 + y/10 = 13` 

⇒ x + 2y = 260   ...(Equation 2)

3. Solve (1) and (2):

From (1): x = 3y – 140

Substitute into (2):

(3y – 140) + 2y = 260 

⇒ 5y – 140 = 260

⇒ 5y = 400 

⇒ y = 80

Then x = 3(80) – 140

 = 240 – 140

= 100

Cost price of the tea-set = ₹ 100 and cost price of the lemon-set = ₹ 80.