A man sells an article for Rs. 840 at a profit of 20%. If he wishes to make a…

Concept: The Selling Price (SP) of an article is obtained by adding the profit percentage to its Cost Price (CP): SP = CP × (1 + profit%/100). So the same relation, reversed, recovers the Cost Price from a known Selling Price and profit percentage: CP = SP ÷ (1 + profit%/100). Once CP is known, it stays fixed and can be used to find the Selling Price needed for any other profit percentage.

Application:

1. Let the cost price of the article be CP.

2. The article is sold for Rs. 840 at a profit of 20%, so 840 = CP × (1 + 20/100) = CP × 1.20.

3. Solving for CP: CP = 840 ÷ 1.20 = Rs. 700.

4. For a profit of only 5%, the required selling price SP2 = CP × (1 + 5/100) = 700 × 1.05.

5. SP2 = Rs. 735.

Cross-check:

At CP = Rs. 700, a 20% profit gives a profit amount of 700 × 20/100 = Rs. 140, so SP = 700 + 140 = Rs. 840 — matching the selling price given in the question. At a 5% profit, the profit amount is 700 × 5/100 = Rs. 35, so SP = 700 + 35 = Rs. 735, independently confirming the result.

Hence, the selling price should be Rs. 735.