Discussion
A shopkeeper bought locks at the rate of 8 locks for ₹ 34 and sold them at the rate of 12 locks for ₹ 57. His percentage gain is
Answer: D
The gain is \(\frac{200}{17}\) per cent, about 11.76%.
Compare the same number of locks, the LCM of 8 and 12, which is 24:
\[ \begin{aligned} \text{CP of 24} &= 3 \times 34 = 102 \\ \text{SP of 24} &= 2 \times 57 = 114 \\ \text{gain} \% &= \frac{12}{102} \times 100 = \frac{200}{17} \end{aligned} \]
Equivalently, each lock costs Rs. 4.25 and sells for Rs. 4.75, a gain of Rs. 0.50 on 4.25. \(\frac{100}{17}\), about 5.9%, is half the true figure, and the other two options do not come from these prices.
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