A shopkeeper marked up the price of article P by 20% and gave a discount of…

Concept

For a single article, the trading chain is fixed: Cost Price (CP) is raised by a markup to get the Marked Price (MP), a discount on the MP gives the Selling Price (SP), and the sign of (SP - CP) decides profit or loss. Two identities drive every such problem: MP = CP x (1 + markup%/100) and SP = MP x (1 - discount%/100). Whatever single discount d makes the books balance for one article can then be reused as data for another.

Application

1. Take CP of article P as 100 (a base for percentages). Markup is 20%, so MP = 100 x 1.20 = 120.

2. A discount of d% gives SP of P = 120 x (1 - d/100) = 120 - 1.2d.

3. P is sold at a loss of (d - 11)%, so SP of P = 100 - (d - 11) = 111 - d.

4. Equate the two expressions for SP of P: 120 - 1.2d = 111 - d.

5. Collect terms: 120 - 111 = 1.2d - d, i.e. 9 = 0.2d, so d = 45.

6. Article Q earns a profit of 1.5d% = 1.5 x 45 = 67.5%.

7. CP of Q = Rs.200, so SP of Q = 200 x (1 + 67.5/100) = 200 x 1.675 = Rs.335.

Cross-check

Verify d = 45 in the loss line: loss% = d - 11 = 34%, so SP of P = 111 - 45 = 66 on a CP of 100 — a 34% loss, exactly as required. Feeding d = 45 forward, the 67.5% profit on Rs.200 lands at Rs.335.