Question

Two bikes were sold for a total of Rs.1,50,000. One bike was sold at \(33\frac{1}{3}\)% loss and the other at 20% profit. The cost price of the first bike is equal to the selling price of the other bike. Find the overall loss.

• A. Rs.10,000
• B. Rs.12,000
• C. Rs.15,000
• D. Rs.18,000

Hint:

Converting percentages to fractions (e.g., \(20% = 1/5\)) simplifies multiplication and division in profit and loss problems.

Answer 1

The Correct Option is C

Step 1: Express profit and loss as fractions and define variables. Let CP1, SP1 be for the first bike and CP2, SP2 for the second. Loss on first bike = \(33\frac{1}{3}% = \frac{1}{3}\). So, \( SP1 = CP1 \times (1 - \frac{1}{3}) = \frac{2}{3}CP1 \). Profit on second bike = 20% = \(\frac{1}{5}\). So, \( SP2 = CP2 \times (1 + \frac{1}{5}) = \frac{6}{5}CP2 \).

Step 2: Use the given conditions to form equations. Condition 1: \( SP1 + SP2 = 1,50,000 \). Condition 2: \( CP1 = SP2 \).

Step 3: Solve the system of equations. Substitute \( CP1 \) for \( SP2 \) in the first equation: \[ SP1 + CP1 = 1,50,000 \] Now substitute \( SP1 = \frac{2}{3}CP1 \): \[ \frac{2}{3}CP1 + CP1 = 1,50,000 \Rightarrow \frac{5}{3}CP1 = 1,50,000 \] \[ CP1 = 1,50,000 \times \frac{3}{5} = 90,000 \] Now find the other values: \( SP2 = CP1 = 90,000 \). From \( SP2 = \frac{6}{5}CP2 \), we get \( 90,000 = \frac{6}{5}CP2 \Rightarrow CP2 = 90,000 \times \frac{5}{6} = 75,000 \).

Step 4: Calculate the total cost price and the overall loss. Total Cost Price = \( CP1 + CP2 = 90,000 + 75,000 = 1,65,000 \). Total Selling Price = Rs.1,50,000. Overall Loss = Total Cost Price - Total Selling Price = \( 1,65,000 - 1,50,000 = 15,000 \).