Vikalp, Nilay and Nilabh and visited a shop to buy LED TV and each one of them bought at least one unit of the TV. The shopkeeper gave a discount of $20 %$ to Vikalp. Nilay, a good bargainer got two successive discounts of $20 %$ and $60 %$ . Nilabh, the hardest bargainer of all got three successive discounts of $20 %$ , $40 %$ and $50 %$ respectively. After selling total of 'x' units to three of them, the shopkeeper calculated that he had given an overall discount of $56 %$ . If
$10 \leq x \leq 20$ , then how many values of 'x' are possible? (Assume every one bought at least one unit).

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Solution

The correct option is B
6

Discount to Nilay = $1 - 0.8 \times 0.4 = 68 %$
Discount to Nilabh = $1 - 0.8 \times 0.6 \times 0.5 = 76 %$

Let a,b,c be the number of units sold to Vikalp, Nilay, and Nilabh respectively.

So, 0.2a+0.68b+0.76c=0.56(a+b+c)

So, 5c=3.(3a-b),

So,c is multiple of 3.
If,c=3 then (a,b)= (2,1),(3,4), (4,7)
If, c=6 then (a,b)= (4,2), (5,5), (6,8)

Hence 6 solutions.

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