The sum of the cost prices of two bikes is Rs50,000. The first bike was sold at a profit of 20% and second bike at a loss of 20%. If
the selling prices are the same, what is the cost price (in Rs) of the second bike?
This questions was previously asked in
SSC MTS 7th October 2021 Shift-3
Explanation:
- The sum of the cost prices of two bikes is Rs 50,000. We can express this as:
\(CP_1 + CP_2 = 50,000\)
- The first bike is sold at a 20% profit. Selling Price (SP) of the first bike is:
\(SP_1 = CP_1 \times 1.2\)
- The second bike is sold at a 20% loss. Selling Price (SP) of the second bike is:
\(SP_2 = CP_2 \times 0.8\)
- Both bikes are sold at the same selling price, so:
\(CP_1 \times 1.2 = CP_2 \times 0.8\)
- Solving these equations simultaneously:
- From \(CP_1 + CP_2 = 50,000\) and \(1.2CP_1 = 0.8CP_2\),
we can write \(CP_1 = 2CP_2/3\).
- Substituting in the first equation:
\(\frac{2}{3}CP_2 + CP_2 = 50,000\)
\(\frac{5}{3}CP_2 = 50,000\)
\(CP_2 = 30,000\)
- Therefore, the cost price of the second bike is Rs 30,000.
- Option: 3 - 30,000 is the correct answer.
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By: santosh