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Question
A briefcase was sold at a profit of 10%. If its cost price was 5% less and it was sold for Rs.120 more, the gain would have been 20%. Find the cost price of the briefcase.
Solution
Let the C.P. of briefcase be Rs.100
Profit = 10%
`"S.P."/"C.P." = 1 + "Profit"/(100)`
⇒ `"S.P."/(100) = 1 + (10)/(100)`
⇒ `"S.P."/(100) = (100 + 10)/(100)`
⇒ S.P. = `(100 xx 110)/(100)`
= Rs.110
When buying at 5% less,
C.P. of the briefcase
= Rs.100 - 5% of Rs.100
= Rs.(100 - 5)
= Rs.95
Gain % = 20%
Gain = `(20)/(100)` x Rs.95
= Rs.19
∴ S.P. of the briefcase
= Rs,95 + Rs.19
= Rs.114
∴ Difference between the two S.P.'s
= Rs.114 - Rs.110
= Rs.4
When the difference in S.P. is Rs.4, the C.P. of the briefcase is Rs.100
∴ When the difference in S.P. is Rs.120, the C.P. of the briefcase is
= Rs.`((100 xx 120)/(4))`
= Rs.3000.
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