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A merchant bought a batch of goods. He fixed the price at 30% above his cost price. He managed to sell half of the stock at this price, one quarter of the stock at a discount of 20% on the marked price and the remainder at a discount of 40% on the marked price. Find his percentage profit on the batch of goods.

My working:

Let $T$ be the total profit on the batch of goods sold at the marked price. Let $mp$ be the marked price and $cp$ be the cost price.

Then

$\frac{1}{2}T=mp-cp$
$\frac{1}{4}T=80\%mp-cp$
$\frac{1}{4}T=60\%mp-cp$

But $mp=130\%cp$

So

$\frac{1}{2}T=130\%cp-cp$
$\frac{1}{4}T=80\%(130\%cp)-cp$
$\frac{1}{4}T=60\%(130\%cp)-cp$

which implies $T=\frac{13}{10}cp-cp+\frac{26}{25}cp-cp+\frac{39}{50}cp-cp$, then $T=\frac{3}{25}cp$. What we got is a loss! The total profit is less than the cost price?

The correct answer is 10.5%.

Could anybody tell me where did I do wrong and how could I fix it?

Is there any easier approach to the problem?

Thanks.

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  • $\begingroup$ Only when SP is less than CP can we say ot is a loss. If profit itself is positive, then there is no loss. $\endgroup$
    – N.S.JOHN
    Commented May 7, 2016 at 12:47

1 Answer 1

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Take total CP as $x$

For half stocks,

CP$=\frac {x}{2}$

SP$=\frac {x}{2}.\frac {13}{10}$

For 1st quater stocks,

CP $=\frac {x}{4}$

SP$=\frac {x}{4}.\frac {13}{10}.\frac {100-20}{100}$

Same goes for 2nd quarter stocks, just with different discount.

You will get total SP = $1.105×x $

which is in agreement with the given answer.

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  • $\begingroup$ I hope you understood where you went wrong. $\endgroup$
    – N.S.JOHN
    Commented May 7, 2016 at 12:43
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    $\begingroup$ yup I got it. Thanks! $\endgroup$
    – user71346
    Commented May 7, 2016 at 12:53

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