Question

A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?

• A. 200
• B. 250
• C. 300
• D. 280

Hint:

When your algebraic solution doesn't match any of the given options, double-check your work. If it's still inconsistent, consider the possibility of a typo in the question's numbers and test if a small change (like 40% to 60%) makes one of the options work.

Answer 1

The Correct Option is B

Step 1: Assume the cost price is a convenient ₹100 first. At 20% profit, \( SP_1 = 120 \).
Step 2: New cost \( =90 \); at 60% profit, \( SP_2 = 90\times1.6 = 144 \).
Step 3: Difference for this assumed cost: \( 144-120=24 \). But the actual difference is ₹60, which is \( \frac{60}{24}=2.5 \) times bigger.
Step 4: Scale the assumed cost by the same factor:
\[ 100 \times 2.5 = \boxed{250}. \]

Final Answer: Cost price \( = ₹250 \). (Option 2)