I guess loss or maybe gain?

Algebra Level 2

I had some of my books which were now no use to me, so I wanted to sell them.

I sold half of them at 40% loss then half of the remaining at 40% gain and the remaining at same price as the selling price.

What was net profit % or loss%.

10% loss 25% gain 25% loss 10% gain

Abhay Tiwari by Abhay Tiwari , 28, India

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2 solutions

Saya Suka
Mar 4, 2021

If we divide the books into quarters, then we have :
1) 25% of 40% loss
2) 25% of 40% loss
3) 25% of 40% gain
4) 25% of 0% profit

2) + 3) will end up as double portion of 4), so our total amount is 25% of 40% loss and 75% of 0% profit. So overall 100% = 25% × 4, therefore our net loss is 40% ÷ 4 = 10%.

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Hung Woei Neoh
Apr 18, 2016

1 2 \dfrac{1}{2} of the books were sold at 40 % 40\% loss, which is − 40 % -40\% profit.

Half of the remaining = 1 2 × 1 2 = 1 4 =\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4} were sold at 40 % 40\% profit.

The remainder = 1 − 1 2 − 1 4 = 1 4 =1 - \dfrac{1}{2} - \dfrac{1}{4} = \dfrac{1}{4} were sold at the same price, which is equivalent to 0 % 0\% profit.

Therefore, the total profit

= 1 2 × − 40 % + 1 4 × 40 % + 1 4 × 0 % = \dfrac{1}{2} \times -40\% + \dfrac{1}{4} \times 40\% + \dfrac{1}{4} \times 0\%

= − 10 % =-10\% profit

which is equivalent to 10 % loss \boxed{10\%\;\text{loss}}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Hung woei Neoh, nice solution, but there is another approach through which it becomes much simpler, try assuming number of goods and their prices and then solve it. BTW, this approach is also good :)

Abhay Tiwari - 5 years, 1 month ago

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