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A vendor bought lemons at 40 for a rupee. How many must he sell for a rupee to gain 25%?
34
36
33
32
32
To gain 25%, the price must increase by factor 1.25. Since quantity is inversely proportional to price for a fixed amount, divide the initial quantity by 1.25: 40 / 1.25 = 40 / (5/4) = 32.
Cost price of 40 lemons = 1 rupee. Desired gain percentage = 25%.
QuantitysellтАЛ=1+Gain%QuantitybuyтАЛтАЛ
To gain 25%, the price must increase by factor 1.25. Since quantity is inversely proportional to price for a fixed amount, divide the initial quantity by 1.25: 40 / 1.25 = 40 / (5/4) = 32.
Most students mistakenly divide the price (1 rupee) by 1.25 and calculate the new price per lemon, then forget to invert it to find the total quantity for a rupee.
Calculate Cost Price of one lemon
If 40 lemons cost 1 rupee, the cost price (CP) of one lemon is 1/40 rupee.
CP=401тАЛ
Determine Selling Price for 25% gain
To gain 25%, the selling price (SP) per lemon must be CP ├Ч 1.25.
SP=401тАЛ├Ч1.25=401тАЛ├Ч45тАЛ=1605тАЛ=321тАЛ
Calculate Quantity for one rupee
Since the SP of one lemon is 1/32 rupee, the vendor must sell 32 lemons to earn 1 rupee.
Quantity=1/321тАЛ=32
D is correct because 40 lemons at 1 rupee requires selling 32 lemons at 1 rupee to achieve a 25% gain.
This concept of inverse proportionality between quantity and price is identical to problems involving speed, time, and distance where speed ├Ч time = constant distance.
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