SOLUTION: Price of sugar is increased by 20% if the expenditure on sugar has to be kept the same as earlier the ratio between the reduction in consumption and the original consumption is?? (

Question 1002078: Price of sugar is increased by 20% if the expenditure on sugar has to be kept the same as earlier the ratio between the reduction in consumption and the original consumption is?? (In short method)
Found 2 solutions by Theo, Vaishnava:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the original consumption.
let y = the original price.
the expenditure is therefore equal to x*Y.

if you raise the new price by 20%, then the new price is equal to 1.2 * y

1.2 * y is the same as 6/5 * y

in order to keep the expenditure the same, the original consumption needs to be divided by 1.2.

divided by 1.2 is the same as multiplying by 1/1.2

multiplying by 1/1.2 is the same as multiplying by 5/6.

if the original price is multiplied by 6/5, the original consumption has to be multiplied by 5/6 in order to keep the total expenditure the same.

you get:

expenditure = x * y

expenditure = 5/6 * x * 6/5 * y = x * y

the expenditure remains the same.

the problem is stated as shown below:

Price of sugar is increased by 20% if the expenditure on sugar has to be kept the same as earlier the ratio between the reduction in consumption and the original consumption is?

they are looking for the ratio between the reduction in consumption and the original consumption.

if the original consumption is x and the reduced consumption is 5/6 * x, then the reduction in consumption is 1/6 * x.

the ratio between the reduction in consumption and the original consumption is therefore 1/6 * x / x which results in 1/6.

Answer by Vaishnava(1) (Show Source): You can put this solution on YOUR website!

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