A rise of 25percentage in the price of grapes compels a person to buy 1.5 kg of grapes less for 240 rupee. Then ,the oroginal price of grapes er kg is ______?
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This is a ratio and proportions problem, with the ratio expressed as a unit rate: Price per weight or Rupees/kg Old unit rate: 240 R x kg the weight 'x' is unknown New unit rate: 240 R times 25% increase = 300 R x kg x kg But, there are only 240 R to spend, so we take the new unit rate, and that is proportional to the lesser amount and the lower weight: 300 R = 240 R x kg x - 1.5 kg Now cross multiply: 300 ( x - 1.5) = x times 240 Use distributive property to eliminate the parentheses: 300x - 450 = 240x Isolate the variable x by subtracting 300x from both sides: - 450 = - 60x Multiply both sides by -1: and solve for x: x = 450/60 = 7.5 kg of sugar originally. 240 rupees/ 7.5 kg = 32 rupees/ kg and the new price is 32 * 1.25 = 40 rupees/kg
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budhianahak1998:
32 rupee per kg
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