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October 6th, 2018, 04:14 AM   #1
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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.
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October 6th, 2018, 04:52 AM   #2
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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.
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October 6th, 2018, 05:12 AM   #3
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Quote:
Originally Posted by skipjack View Post
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 ?
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October 6th, 2018, 05:25 AM   #4
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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%.
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October 6th, 2018, 10:12 AM   #5
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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.
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October 7th, 2018, 11:51 PM   #6
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Quote:
Originally Posted by skipjack View Post
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?
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October 8th, 2018, 12:29 AM   #7
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Quote:
Originally Posted by Ganesh Ujwal View Post
How you got 0.8333 and 1.1667?
5/6 and 7/6, as per your original post....
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October 8th, 2018, 01:47 AM   #8
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Quote:
Originally Posted by Denis View Post
u = 1 / (1 - p/100)
v = 1 / (1 + p/100)
What does u and v indicate ?
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October 8th, 2018, 04:05 AM   #9
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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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