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Question 14 : A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

  1. 35
  2. 31
  3. 22
  4. 25

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Explanatory Answer

Let the price of Sugar per kilogram be 'x' rupees.

The man marks it up by 20% and sells 5 kilograms.
Marked Price = 1.2 × x = 1.2x
Therefore, the sale price of these 5 kgs totally would be = 5 × 1.2 × x = 6x
He then gives a discount of 10% on the markup and sells 15 kgs at that price. So, the price per kg now would be 0.9 × 1.2 × x = 1.08x
Therefore, the sale price of these 15 kgs totally would be = 15 × 1.08x = 16.2x
He then looses 3 kgs of Sugar
Therefore, the sale price of these 3 kgs = 0.

There is 35 - 5 - 15 - 3 = 12 kgs of sugar remaining.
Let's say it is sold at px price.
So, the sale price of these 12 kgs will be = 12 × px

The overall profit for the Man is 15%, So the Sale Price of the entire 35 kgs is 35 × 1.15 × x = 40.25x

Summing up and equating all the sale prices...
40.25x = 6x + 16.2x + 0x + 12 × px
40.25x = 22.2x + 12 × px
18.05x = 12 × px

Let's approximate this to
18x = 12 × px p = \\frac{3}{2}) = 1.5

Very importantly, px is attained after marking up the marked price.
Therefore, px = y × Marked Price
1.5x = y × 1.2x
y = \\frac{5}{4}) = 1.25

In other words we can say that the marked price was increased by 25%.


The answer is, "25"

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