
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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October 6th, 2018, 03:14 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 332 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 03:58 AM. 
October 6th, 2018, 03:52 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
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, 04:12 AM  #3  
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  Quote:
What is that formula you have used to calculate overall loss percentage ?  
October 6th, 2018, 04:25 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
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, 09:12 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 
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 09:16 AM. 
October 7th, 2018, 10:51 PM  #6 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  
October 7th, 2018, 11:29 PM  #7 
Senior Member Joined: Apr 2014 From: UK Posts: 886 Thanks: 326  
October 8th, 2018, 12:47 AM  #8 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  
October 8th, 2018, 03:05 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
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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