A seller bought three different types of mobile covers, C1, C2, and C3. The ratio of their selling prices was 3:4:5. He made a profit of 25% on C1, 10% on C2, but incurred a loss of 20% on C3. What was his approximate percent gain or loss in the entire transaction?
loss of 2.33%
Let SPs be 3k, 4k, 5k.
Step 1 – Find each cost price using \(CP = \dfrac{SP}{1 + \text{profit fraction}}\):
\(CP_1 = \dfrac{3k}{1.25} = 2.4k\)
\(CP_2 = \dfrac{4k}{1.10} \approx 3.6364k\)
\(CP_3 = \dfrac{5k}{0.80} = 6.25k\) (loss → divide by 0.80)
Step 2 – Totals:
Total SP = \(3k + 4k + 5k = 12k\)
Total CP = \(2.4k + 3.6364k + 6.25k = 12.2864k\)
Step 3 – Overall: Total CP > Total SP, so it's a loss.
\(\text{Loss}\% = \dfrac{12.2864k - 12k}{12.2864k} \times 100 \approx 2.33\%\)
Hence the seller incurs a loss of approximately 2.33%.
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