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Question
A man buys two cycles for a total cost of Rs.8000. By selling one cycle at a loss of 20% and the other at a profit of 30%, he makes a profit of Rs.650 on the whole transaction. Find the cost price of each cycle.
Solution
Let the cost price of one of the cycles be Rs.x
∴ The cost price of the other cycle = Rs(8000 - x)
For the first cycle,
C.P. = Rs.x
Loss = 20%
Loss
= 20% of Rs. x
= Rs.0.20x
For the second cycle,
C.P. = Rs(8000 - x)
Profit = 30%
∴ Profit
= 30% of Rs.(8000 - x)
= Rs. 0.3(8000 - x)
= Rs. (2400 - 0.3x)
Given, overall profit = Rs.650
∴ (2400 - 0.3x) - 0.2x
= 650
⇒ 0.5x = 2400 - 650
= 1750
∴ x = `(1750)/(0.5)`
= 3500
C.P. of 1st cycle = Rs.3500
C.P. of 2nd cycle
= Rs.8000 - Rs.3500
= Rs.4500.
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