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Question
A briefcase was sold at a profit of 15%. If its cost price was 5% less and it was sold for Rs.35 less, the gain would have been 20%. Find the cost price of the briefcase.
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Solution
Let the C.P. of the briefcase is Rs. x
Profit = 15%
S.P. = C.P. + profit
= Rs. x + 15% of Rs. x
= Rs.1.15x
In the later case, C.P.
= Rs. x - 5% of Rs. x
= Rs. 0.95x
S.P. = Rs.(1.15x - 35)
∴ Gain = S.P. - C.P.
= Rs.(1.15x - 35) - Rs.0.95x
= Rs.(0.2x - 35)
Gain % = 20%
⇒ `"gain"/"C.P." xx 100` = 20
⇒ `((0.2x - 35)/(0.95x)) xx 100` = 20
⇒ `((0.2x - 35)/(0.95x))` = 0.20
⇒ 0.2x - 35 = 0.19x
⇒ 0.01x = 35
⇒ x = 3500
∴ C.P. of the briefcase is Rs.3500.
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