SOLUTION: The price of sugar increases by 32%.a family reduce its consumption so that the expenditure of the sugar is up by10% only.if the consumption of sugar before price rise was 10kg/mo

Question 1124466: The price of sugar increases by 32%.a family reduce its consumption so that the expenditure of the sugar is up by10% only.if the consumption of sugar before price rise was 10kg/month,then the consumption of sugar per month at present in kg is
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

in general, total cost is equal to the quantity bought * the price per unit of quantity bought.

when the quantity is 10 kilograms, and the price is x per kilogram, then the total cost is 10 * x.

if the price goes up 32%, then the total cost becomes 10 * 1.32 * x = 13.2 * x.

but the family wants the total cost to be only 10% higher.

in other words, they want the total cost to be equal to 11 * x.

the new price per kilogram will still be 1.32.

the quantity, however, can be reduced so the total cost is 1.10 * x.

let y = the new quantity.

you get y * 1.32 * x = 11 * x.

divide both sides of this equation by 1.32 * x to get:

y = (11 * x) / (1.32 * x)

simplify to get y = 11 / 1.32 = 8.33333..... = 8 and 1/3 kilograms.

if they reduce the quantity from 10 kilograms to 8 and 1/3 kilograms, then the overall cost will only be 10% higher rather than 32% higher.

8 and 1/3 * 1.32 * x = 11 * x.

the total cost went up from 10 * x to 11 * x.

that's a 10% increase in total cost.

as an example, assume the original price per kilogram was 5 dollars.

the family buys 10 kilogram * 5 dollars per kilogram = 50 dollars.

the price goes up 32% so the price is now 6.6 dollars per kilogram.

the family reduces their consumption to 8 and 1/3 kilograms.,

the new total cost is 8 and 1/3 * 6.6 = 55 dollars.

that's a 10% increase in total cost because (55 - 50) / 50 = 5 / 10 = .1 = 10%.

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