Question : The price of a bicycle is marked by a trader at Rs. 1000. He sold the bicycle allowing successive discounts of 20%, 10% and 5%. Thus the trader gained 14%, then the cost price of the bicycle (in rupees) is:
Option 1: Rs. 790
Option 2: Rs. 600
Option 3: Rs. 560
Option 4: Rs. 510
Correct Answer: Rs. 600
Solution :
Let the marked price be MP, the cost price be CP, the selling price be SP, and the $D_1, D_2,$ and $D_3$ be successive discount percentages.
Given that the marked price of the bicycle is Rs. 1000.
MP = Rs. 1000
The trader sold the bicycle allowing successive discounts of 20%, 10%, and 5%.
For three successive discounts SP = $\frac{100-D_1}{100}× \frac{100-D_2}{100}× \frac{100-D_3}{100}×$ MP
So, SP = MP × (1 – 0.20) × (1 – 0.10) × (1 – 0.05)
= 1000 × 0.80 × 0.90 × 0.95 = Rs. 684
Given that the trader gained 14%,
$CP= \frac{684}{100+14}\times 100 = 600$
Hence, the correct answer is Rs. 600.
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