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Question
A bought a cycle and spent Rs.110 on its repair. He then sold it to B at 20% profit. B sold it to C at 10% loss. C sold it for Rs.1188 at 10% profit. How much did A pay for the article?
Solution
Let A buy the cycle for Rs. x.
For A, C.P. of the cycle = Rs. x + Rs. 110
Profit = 20%
`"S.P."/"C.P." = 1 + "Profit"/(100)`
⇒ `"S.P."/(x + 110) = 1 + (20)/(100)`
⇒ `"S.P."/(x + 110) = (100 + 20)/(100)`
⇒ S.P. = `(120)/(100) (x + 100)`
= Rs.`(12)/(10)(x + 110)`
For B, C.P. of the cycle = Rs.`(12)/(10)(x + 110)`
Loss = 10%
`"S.P."/"C.P." = 1 - "Loss"/(100)`
⇒ `"S.P."/(12/10(x + 110)) = 1 - (10)/(100)`
⇒ `"S.P."/(12/10(x + 110)) = (100 - 10)/(100)`
⇒ S.P. = `(90)/(100) (12)/(10) (x + 110)`
= Rs. `(9)/(10).(12)/(10)(x + 110)`
For C, C.P. of the cycle
= Rs. `(9)/(10).(12)/(10)(x + 110)`
Profit = 10%
S.P. of the cycle
= Rs.`(1 + 10/100) (9)/(10).(12)/(10)(x + 110)`
= Rs. `(11)/(10).(9)/(10).(12)/(10)(x + 110)`
ATQ, `(11)/(10).(9)/(10).(12)/(10)(x + 110)`
= 1188
⇒ x + 110 = 1000
⇒ x = 1000 - 110
= 890
∴ A paid Rs.890 for the cycle.
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