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# Percentage

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Intern
Joined: 14 Sep 2017
Posts: 2

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30 Sep 2017, 23:01
A trader normally makes a profit of 40% on items he sells. If he reduces the price by 10%, his sales increase by 40%. Let X be the total profit when he does not reduce the price , and Y the total profit of when he reduces the price . What is the ratio of Y to X ?

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Intern
Joined: 26 Jul 2017
Posts: 18
Location: India

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01 Oct 2017, 07:22
Harvardmaniac wrote:
A trader normally makes a profit of 40% on items he sells. If he reduces the price by 10%, his sales increase by 40%. Let X be the total profit when he does not reduce the price , and Y the total profit of when he reduces the price . What is the ratio of Y to X ?

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Let the cost price of the item be p
thus the selling price, which is fetching 40% profit, will be 1.40p
lets say at this price he sells a total of n items
thus his total profit will be X = Revenue - Total Cost = 1.4pn - pn = 0.4pn

Now, The selling price is being reduced by 10%
therefore new selling price will be = 1.4p * .9 = 1.26p
Now the sales quantity is also getting increased by 40%
thus new quantity of sold items is 1.4n
New profit Y = 1.26p * 1.4n - pn = (1.764-1)pn

So X/Y = 0.4pn/0.764pn = 0.5 (approximately)

therefore Y/X will be 2 (approx)
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04 Oct 2017, 20:58
Harvardmaniac wrote:
A trader normally makes a profit of 40% on items he sells. If he reduces the price by 10%, his sales increase by 40%. Let X be the total profit when he does not reduce the price , and Y the total profit of when he reduces the price . What is the ratio of Y to X ?

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Assume S is the sales before the price is reduced.
X = (2/5) x S

If the price is reduced by 10%, 30/90 of the reduced price is the profit.
When the priced is reduced by 10%, the sales is increased by 40%, that is, y = (1/3)S x 1.4 = (1/3)*(7/5)S

Thus the ration of Y to X is (1/3)(7/5)/(2/5) = 7/6 = 1.165.
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Re: Percentage &nbs [#permalink] 04 Oct 2017, 20:58
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