On selling a tea-set at 5% loss and a lemon set at 15% gain, a crockery seller…
2016
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. The cost price of the lemon set is:
- A.
₹80
- B.
₹100
- C.
₹120
- D.
₹115
Attempted by 41 students.
Show answer & explanation
Correct answer: A
Concept. When an item is sold at a percentage profit or loss, the rupee gain or loss equals that fraction of its cost price. If two items with cost prices x and y are sold together, the net rupee gain is the algebraic sum of the individual gains/losses: (rate on x)·x + (rate on y)·y, where a loss carries a negative rate. Two such selling scenarios give two linear equations in x and y, which can be solved simultaneously.
Application. Let the cost price of the tea-set be x and of the lemon set be y.
Scenario 1 — tea-set at 5% loss, lemon set at 15% gain, net gain ₹7: −0.05x + 0.15y = 7.
Scenario 2 — tea-set at 5% gain, lemon set at 10% gain, net gain ₹13: 0.05x + 0.10y = 13.
Add the two equations so the x-terms cancel: (−0.05x + 0.05x) + (0.15y + 0.10y) = 7 + 13, giving 0.25y = 20.
Solve for y: y = 20 ÷ 0.25 = 80.
Cross-check. Substitute y = 80 into Scenario 2: 0.05x + 0.10(80) = 13 → 0.05x + 8 = 13 → x = 100. Check Scenario 1: −0.05(100) + 0.15(80) = −5 + 12 = 7 ✓. Both scenarios hold, so the lemon set costs ₹80.