cost of 1 kg of right increased by 25% radha reduced his monthly consumption by 24% also the cost of 1 kg of weight decrease by 20% increase his monthly consumption by 30% if the total quantity of food grains radha consumes and expenditure on them remain same what is the ratio of the cost of weak to the cost of rice
Answers
Given : cost of 1 kg of rice increased by 25% radha reduced his monthly consumption by 24% also the cost of 1 kg of wheat decrease by 20% increase his monthly consumption by 30%
the total quantity of food grains radha consumes and expenditure on them remain same
To Find : Ratio of the cost of wheat to the cost of rice
Solution:
Let say Cost of Rice per kg = x Rs/kg
Consumption of Rice = R kg
Expenditure on Rice = RX Rs
Let say Cost of Wheat per kg = y Rs/kg
Consumption of Wheat = W kg
Expenditure on Wheat = Wy Rs
Total consumption = R + W kg
Total Expenditure = Rx + Wy Rs
New cost of Rice = x + (25/100)x = 1.25x Rs/kg
New Consumption of Rice = R - (24/100)R = 0.76R kg
New Expenditure on Rice = 1.25x * 0.76R = 0.95 Rx Rs
New cost of Wheat = y - (20/100)y = 0.8y Rs/kg
New Consumption of Wheat = W + (30/100)W = 1.3W kg
New Expenditure on Wheat = 0.8y * 1.3W = 1.04Wy Rs
Total New consumption = 0.76R + 1.3W kg
Total New Expenditure = 0.95Rx + 1.04Wy Rs
R + W = 0.76R + 1.3W
=> 0.24R = 0.3W
=> 4R = 5W
=> R = 1.25W
Rx + Wy = 0.95Rx + 1.04Wy
=> 0.05Rx = 0.04Wy
=> 0.05(1.25W)x = 0.04Wy
=> x/y = 4/6.25
=> x/y = 16/25
=> y /x = 25/16
ratio of the cost of wheat to the cost of rice = 25 : 16
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