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CAT Exam Model Paper 5 with solutions for free online practice

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Question : 8 of 60

Marks: +1, -0

Vijay, Saral and Himanshu visited a shop to buy a certain article and each one of them bought atleast one unit of the article. The shopkeeper gave a discount of 20% to Vijay, two successive discounts of 20% and 25% to Saral and three successive discounts of 20%, 25% and 40% to Himanshu. After selling ‘x’ units of the article he calculated that he had given an overall discount of 50%. If 8 ≤ x ≤ 20 , then how many values of ‘x’ are possible?

5
7
0
None of these

Solution:

Discount to Saral =

20 + 25 - \frac{20 \times 25}{100} = 40\%

Discount to Himanshu =

= 40 + 40 - \frac{40 \times 40}{100} = 64\%

Let a, b, c be the number of units sold at 20%, 40% and 64% respectively.

\Rightarrow \frac{a\times 20}{100} + b\times 40 100 + c\times 64 100 = (a+b+c)50 100

\Rightarrow \frac{7c}{50} - \frac{b}{10} - \frac{3a}{10} = 0

\Rightarrow 7c - 5b - 15a = 0

So ‘c’ has to be a multiple of 5.

Values of a, b, c satisfying the equation are (2,1,5); (1,4, 5); (4, 2, 10); (3, 5, 10); (2, 8, 10).

Hence the possible values for x are 8, 10, 16, 18 and 20.

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