If the price of each book goes up by ₹ 5, then Asha can buy 20 books less for ₹ 1200. Find the original…
The correct choice is: “₹ 15, 80” Let the original price be ₹ p. Then 1200/p − 1200/(p + 5) = 20. So 1200 × 5 = 20p(p + 5), i.e. p² + 5p − 300 = 0, i.e. (p + 20)(p − 15) =…
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If the price of each book goes up by ₹ 5, then Asha can buy 20 books less for ₹ 1200. Find the original price and the number of books Asha could buy at the original price.
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Correct answer C
The correct choice is: “₹ 15, 80”
Let the original price be ₹ p. Then 1200/p − 1200/(p + 5) = 20.
So 1200 × 5 = 20p(p + 5), i.e. p² + 5p − 300 = 0, i.e. (p + 20)(p − 15) = 0, giving p = 15.
At ₹ 15 she buys 1200/15 = 80 books; at ₹ 20 she buys 60, which is 20 fewer. ✔
“₹ 20, 60” gives the new price and number, not the original; “₹ 25, 50” and “₹ 10, 90” are not consistent (25 × 50 = 1250 and 10 × 90 = 900, not 1200).
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