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Question

A shopkeeper buys a number of books for ₹40. If he had bought 2 more books for the same amount, then each book would have cost him ₹1 less. The number of books he bought is

A
10
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B
8
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C
12
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D
16
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Solution

The correct option is B 8Let the shopkeeper buys x number of books. According to the question: Cost of x books =₹40 ∴ Cost of each book =₹40x Again, when he had bought 2 more books for the same amount then, the cost of each book =₹40x+2 Thus, according to the given condition 40x−40x+2=1 ⇒40(x+2)−40xx(x+2)=1 ⇒40x+80−40xx(x+2)=1 ⇒80=x2+2x ⇒x2+2x−80=0 ⇒x2+10x−8x−80=0 ⇒x(x+10)−8(x+10)=0 ⇒(x−8)(x+10)=0 ⇒x=8,−10 Neglecting the negative value, the number of books he bought is 8. Hence, the correct answer is option (2).

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