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 October 6th, 2018, 04:14 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 343 Thanks: 1 Is there any trick to solve it? A man sells 2 cycles for Rs 7035 each, one at a loss of 16.67% and the other at a gain of 16.67%. What is his overall gain/loss %? Solution: Ist cycles SP = 7035 CP = ? Loss =16.67% = 5/6 IInd cycle SP = 7035 C.P = ? Profit =16.67% = 7/6 We get SP = 35 by multiply numerator of loss and profit fractions. CP1 = 35*6/5 = 42 CP2 = 35*6/7 = 30 Sum of SP = 70 Sum of CP = 72 Loss = 2 Loss% = 2/7 * 100 = 2.78% I am following this method to solve. Is there any easy method exist for this problem? Last edited by skipjack; October 6th, 2018 at 04:58 AM.
 October 6th, 2018, 04:52 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,262 Thanks: 1958 Total cost price = Rs 7035/0.8333 + Rs 7035/1.1667 = Rs 14472.17 after rounding to 2 d.p. Overall loss percentage = (100(1 - (7035 + 7035)/14472.17))% = 2.7789% approximately.
October 6th, 2018, 05:12 AM   #3
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Quote:
 Originally Posted by skipjack Total cost price = Rs 7035/0.8333 + Rs 7035/1.1667 = Rs 14472.17 after rounding to 2 d.p. Overall loss percentage = (100(1 - (7035 + 7035)/14472.17))% = 2.7789% approximately.
What is the meaning of 2 d.p?

What is that formula you have used to calculate overall loss percentage ?

 October 6th, 2018, 05:25 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,262 Thanks: 1958 The meaning of "2 d.p." is "2 decimal places". If one assumes that the 16.67% given in the question was an approximation of exactly (100/6)%, the loss percentage becomes exactly (25/9)%, which is 2.7778% approximately. The formula is loss percentage = (1 - SP/CP)100% (or equivalently 100(1 - SP/CP)%). If SP/CP > 1, the gain percentage is (SP/CP - 1)100%.
 October 6th, 2018, 10:12 AM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,938 Thanks: 984 Since selling price does not matter (as long as same for both), then easier to make it 1 (instead of 7035). Then solution is quite simplified: p = 16+2/3 (given) u = 1 / (1 - p/100) v = 1 / (1 + p/100) overall = 100[2(u + v) - 1] = -2.777777.......% Last edited by Denis; October 6th, 2018 at 10:16 AM.
October 7th, 2018, 11:51 PM   #6
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Quote:
 Originally Posted by skipjack Total cost price = Rs 7035/0.8333 + Rs 7035/1.1667 = Rs 14472.17 after rounding to 2 d.p.
loss% and gain% is 16.67% i.e 16.67/100 which equals to 0.1667.
How you got 0.8333 and 1.1667?

October 8th, 2018, 12:29 AM   #7
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Quote:
 Originally Posted by Ganesh Ujwal How you got 0.8333 and 1.1667?
5/6 and 7/6, as per your original post....

October 8th, 2018, 01:47 AM   #8
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Quote:
 Originally Posted by Denis u = 1 / (1 - p/100) v = 1 / (1 + p/100)
What does u and v indicate ?

 October 8th, 2018, 04:05 AM #9 Global Moderator   Joined: Dec 2006 Posts: 20,262 Thanks: 1958 Denis used u for CP/SP calculated when a loss occurred, and v for CP/SP calculated when a gain occurred.

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