The price of sugar having gone down by 20% one can buy 6.4kg more for Rs 512. Find the ratio between the original and the reduced price (per kg)?

Let the original price by Rs x Reduced price = Rs (80x/100) ∴512/(80 x/100) - 512/x = 6.4 ⇒51200/80x - 512/x = 6.4 ⇒640/x - 512/x = 6.4 =>128/x= 6.4 ∴ x = 128/6.4 = 20 Original price = Rs 20 Reduced price = Rs (80/100) × 20 = Rs 16 ∴ Required ratio = 20:16 = 5:4

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