Discussion
By selling a car for Rs. 54,000 a car-seller gains 20%, then the cost price for the car is
Answer: D
The cost price is Rs. 45,000.
A 20% gain means the selling price is 120% of the cost price:
\[ \begin{aligned} 1.2 \times \text{CP} &= 54000 \\ \text{CP} &= 45000 \end{aligned} \]
Check: 20% of 45,000 is 9,000, and 45,000 + 9,000 = 54,000. Rs. 43,200 would come from wrongly taking 20% off the selling price, and the other options do not give a 20% gain.
In general, \(\text{CP} = \text{SP} \times \frac{100}{100 + \text{gain}\%}\), here \(54000 \times \frac{100}{120} = 45000\).
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