CAT 2020 Question Paper | Quants Slot 3

CAT Previous Year Paper | CAT Quants Questions | Question 14

CAT Exam historically tested Profit and loss in every edition of CAT Exam. With every passing year, CAT Exam has increased the importance of Arithmetic questions from topics such as Profit and Loss. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score.

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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