If the price of rice falls by 2½ %, a person can buy 9 kg more of rice for Rs. 1,260 than before. If the price had risen 12½ %, how much rice would he have bought for the same sum?
Explanation:
Let the initial price per kg and quantity be p and q respectively. ⇒ p × q = 1260 ...(1)
Now, when price falls 2.5%, new price will be 0.975p and new quantity bought = q + 9 ⇒ 0.975p × (q - 9) = 1260 ...(2)
(1) = (2) ⇒ 0.975p × (q - 9) = p × q ⇒ 0.975(q - 9) = q ⇒ 0.975 × 9 = 0.025q ⇒ q = 351 kgs.
Now, if price rises by 12.5%, new price will be 1.125p and let the new quantity be x. ⇒ 1.125p × x = 1260 = p × q ⇒ 1.125 × x = 351 ⇒ x = 351/1.125 = 312 kgs.
Hence, option (b).
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