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

To solve this problem, we need to determine the cost price (CP) of the item. Let's go through the steps:

Step 1: Establish initial conditions

Let the original cost price of the item be \(C\). The item is sold at a profit of 20%, so the selling price (SP) is:

\(\text{SP} = C + 0.2C = 1.2C\)

Step 2: Establish conditions with new scenario

In the second scenario, if the cost price is 10% less, it becomes:

\(C' = C - 0.1C = 0.9C\)

If he sells it for ₹60 more than the original selling price, the new selling price becomes:

\(\text{New SP} = 1.2C + 60\) 

In this case, the profit is 60%, so the new selling price would also be:

\(\text{New SP} = 0.9C + 0.6(0.9C) = 0.9C + 0.54C = 1.44C\)

Step 3: Equate and solve for C

We have two equations for the new selling price:

\(1.2C + 60 = 1.44C\)

Simplify the equation:

\(60 = 1.44C - 1.2C \\ 60 = 0.24C\)

Solving for \(C\):

\(C = \frac{60}{0.24} = 250\)

Conclusion:

The original cost price of the item is ₹250.

Verification:

Let's check:

• Original SP = \(1.2 \times 250 = 300\)
• New cost price \((C') = 0.9 \times 250 = 225\)
• New SP should be \((1.44 \times 250 = 360)\) as per 60% profit, which matches the calculation.

Hence, the calculations and the derived cost price are correct.