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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 October 6th, 2018, 03:14 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 476 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: 21,026 Thanks: 2257 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
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 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, 04:25 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 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: 14,597 Thanks: 1039 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
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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 7th, 2018, 11:29 PM   #7
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 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, 12:47 AM   #8
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 Originally Posted by Denis u = 1 / (1 - p/100) v = 1 / (1 + p/100)
What does u and v indicate ? October 8th, 2018, 03:05 AM #9 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 Denis used u for CP/SP calculated when a loss occurred, and v for CP/SP calculated when a gain occurred. Tags obtained, solve, trick, values Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post kiwis Elementary Math 5 February 9th, 2016 07:21 PM stainburg Real Analysis 4 June 3rd, 2013 11:05 PM

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