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

• A. Tea set Rs. 180, Lemon set Rs. 120
• B. Tea set Rs. 130, Lemon set Rs. 70
• C. Tea set Rs. 90, Lemon set Rs. 100
• D. Tea set Rs. 100, Lemon set Rs. 80

To solve the problem, let's denote the cost price of the tea set as T and the cost price of the lemon set as L.

Setting Up the Equations

From the information provided, we can create two equations based on the selling scenarios:

• When the tea set is sold at a 5% loss and the lemon set at a 15% gain, the total gain is Rs. 7:
• Equation 1: -0.05T + 0.15L = 7
• When the tea set is sold at a 5% gain and the lemon set at a 10% gain, the total gain is Rs. 13:
• Equation 2: 0.05T + 0.10L = 13

Solving the Equations

Now, let's solve these equations step by step.

From Equation 1:

Rearranging gives:

0.15L = 7 + 0.05T

L = (7 + 0.05T) / 0.15

Substituting into Equation 2:

Replace L in Equation 2:

0.05T + 0.10((7 + 0.05T) / 0.15) = 13

Multiplying through by 0.15 to eliminate the fraction:

0.0075T + 0.10(7 + 0.05T) = 1.95

Expanding and simplifying:

0.0075T + 0.70 + 0.005T = 1.95

0.0125T = 1.25

T = 100

Finding L:

Substituting T back into the equation for L:

L = (7 + 0.05 * 100) / 0.15 = (7 + 5) / 0.15 = 12 / 0.15 = 80

Final Prices

The actual prices are:

• Tea set: Rs. 100
• Lemon set: Rs. 80

The correct answer is Option D: Tea set Rs. 100, Lemon set Rs. 80.