To make a profit of 20%, the selling price of a good is Rs. 240. What is the cost price of the good?

Introduction / Context:
This is a basic reverse-percentage question. You are given the selling price of a good and the profit percentage, and you must work backwards to obtain the cost price. This type of question strengthens your understanding of how profit percentage relates selling price and cost price, and it appears in almost every competitive exam that tests profit and loss concepts.

Given Data / Assumptions:
- Selling price (SP) of the good = Rs. 240. - Profit percentage = 20%. - Profit is calculated on cost price. - We must find the cost price (CP) of the good.

Concept / Approach:
A profit of 20% means that the selling price is 120% of the cost price. In equation form, SP = CP * (1 + 20 / 100) = CP * 1.20. Therefore CP = SP / 1.20. This is a direct formula approach: whenever you are given selling price and profit percentage, divide the selling price by (1 + profit percentage / 100) to get the cost price. This avoids unnecessary extra steps.

Step-by-Step Solution:
Step 1: SP = Rs. 240 and profit percentage = 20%. Step 2: Express profit percentage as a multiplier: 1 + 20 / 100 = 1.20. Step 3: Use the relation SP = 1.20 * CP. Step 4: Rearranging, CP = SP / 1.20. Step 5: Substitute SP = 240 to get CP = 240 / 1.20. Step 6: CP = 200 rupees.

Verification / Alternative check:
Check by forwarding calculation: if CP = 200, then a 20% profit is 0.20 * 200 = 40. The selling price would then be 200 + 40 = 240, which matches the given selling price. This confirms that the cost price of Rs. 200 is correct.

Why Other Options Are Wrong:
If CP were Rs. 210, then a 20% profit would produce SP = 252, not 240. A cost price of Rs. 220 would give SP = 264, and Rs. 230 would give SP = 276. None of these selling prices match the given 240. Therefore only Rs. 200 is consistent with a 20% profit and a selling price of 240.

Common Pitfalls:
A common mistake is to calculate 20% of the selling price instead of the cost price and then subtract it, which leads to an incorrect answer. Another error is to reverse the fraction and multiply instead of divide. To avoid confusion, always write the relationship explicitly as SP = CP * (1 + profit percentage / 100) and then solve for CP using algebraic steps.

Final Answer:
The cost price of the good is Rs. 200.