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Question
A vendor bought toffees at 6 for Rs.10. How many for Rs.10 must he sell to gain 20%?
Solution
The vendor bought toffees at the rate of 6 for ₹ 10
∴ The cost price of one toffee = `10/6`
i.e. C.P. = `10/6` .............(i)
Let x be the number of toffees he must sell in ₹ 10 to gain 20%
∴ i.e. S.P. = `10/"x"` .............(ii)
Profit percentage = `("S.P". - "C.P")/"C.P"`
Using (i) and (ii) we have
`20% = (10/"x" - 10/6)/(10/6)`
∴ `20/100 = 10(1/"x" - 1/6) xx 6/10`
∴ `1/5 = (1/"x" - 1/6)6`
∴ `1/"x" - 1/6 = 1/30`
∴ `(6 - "x")/(6"x") = 1/30`
∴ 30(6 - x) = 6x
∴ 180 - 30x = 6x
∴ 36x = 180
∴ x = 5
The vendor must sell 5 toffees for ₹ 10 in order to gain 20%
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