Question

A person buys two watches for Rs.1000 in total. He sells one watch at a loss of 5% and the other at a gain of 20%. On the whole, he gains Rs.50. Find the cost prices of the two watches.

• A. Rs.700 and Rs.300
• B. Rs.500 and Rs.500
• C. Rs.600 and Rs.400
• D. Rs.450 and Rs.550

Hint:

When different profit and loss percentages are involved, assume one cost price as a variable and use total selling price to form a single equation.

Answer 1

The Correct Option is C

Step 1: Assume the cost prices of the two watches.
Let the cost price of the first watch be Rs.$x$.
Then the cost price of the second watch will be Rs.$(1000 - x)$.
Step 2: Calculate selling price of the first watch.
The first watch is sold at a loss of 5%.
Therefore, selling price of the first watch is:
\[ \text{SP}_1 = 0.95x \]
Step 3: Calculate selling price of the second watch.
The second watch is sold at a gain of 20%.
Therefore, selling price of the second watch is:
\[ \text{SP}_2 = 1.20(1000 - x) \]
Step 4: Use the condition of overall gain.
Total gain is Rs.50, so total selling price is:
\[ 1000 + 50 = 1050 \]
Step 5: Form the equation using total selling price.
\[ 0.95x + 1.20(1000 - x) = 1050 \]
Step 6: Simplify the equation.
\[ 0.95x + 1200 - 1.20x = 1050 \]
\[ -0.25x + 1200 = 1050 \]
\[ -0.25x = -150 \]
Step 7: Solve for $x$.
\[ x = 600 \]
Step 8: Find the cost price of the second watch.
\[ 1000 - 600 = 400 \]
Step 9: Final conclusion.
Hence, the cost prices of the two watches are Rs.600 and Rs.400 respectively.