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A vendor sold 10 toffees for a rupee, thereby gaining 20%. How many did he buy for a rupee?
6
12
10
8
12
To find the number of items bought per rupee, divide the selling quantity by (1+Gain%/100). Here, 10/1.2=8.33, wait: CP┬аof┬а1┬аtoffee=10├Ч1.21тАЛ=121тАЛ, so 12 toffees for a rupee.
Selling price of 10 toffees = 1 rupee, Gain percentage = 20%
CP=1+100Gain%тАЛSPтАЛ
To find the number of items bought per rupee, divide the selling quantity by (1+Gain%/100). Here, 10/1.2=8.33, wait: CP┬аof┬а1┬аtoffee=10├Ч1.21тАЛ=121тАЛ, so 12 toffees for a rupee.
Many students directly calculate 20% of 10 toffees (which is 2) and subtract it to get 8, forgetting that gain is on price, not on quantity.
Analyze Given Data
The vendor sells 10 toffees for 1 rupee and makes a 20% profit.
SP10тАЛ=Re.┬а1,┬аProfit=20%
Find Selling Price of One Toffee
The selling price of 1 toffee is calculated as SP=101тАЛ rupee.
SP1тАЛ=101тАЛ
Calculate Cost Price of One Toffee
Using the relation between Cost Price and Selling Price at 20% profit: CP1тАЛ=1+Gain%/100SP1тАЛтАЛ.
CP1тАЛ=1.21/10тАЛ=121тАЛ
Determine Number of Toffees Bought per Rupee
Since the cost price of 1 toffee is 121тАЛ rupee, the vendor bought 12 toffees for 1 rupee.
Number┬аof┬аtoffees=12
B is correct because calculating the cost price per toffee gives 121тАЛ of a rupee, which means the vendor bought 12 toffees for a rupee.
Similar inverse proportional relationships between quantity and price appear frequently in time-work and speed-distance problems.