CAT Exam Model Paper 5 with solutions for free online practice

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

Validate

Solution:

Discount to Saral =

20 + 25 - { 20 × 25 }/ { 100 } = 40 \%

Discount to Himanshu =

= 40 + 40 - \ { 40×40 } /{ 100 } = 64 \%

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

⇒{ a×20 } /{ 100 } + { b×40 } { 100 } + { c \× 64 } { 100 } = { ( a + b + c ) 50 } { 100 }

⇒ { 7 c }/ { 50 } - { b } /{ 10 } - { 3 a } /{ 10 } = 0

⇒ 7 c - 5 b - 15 a = 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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