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Question
The price of sugar is increased by 20%. By what percent must the consumption of sugar be decreased so that the expenditure on sugar may remain the same?
Solution
Let price of x kg of sugar = Rs. 100
Increase in price = 20%
∴ New price = 100 + 20 = Rs.120
∴ For Rs. 120, sugar obtained = x kg.
For Rs. 100, sugar obtained
= `x/(120) xx 100`
= `(5x)/(6)"kg"`
Original consumption = x kg
New consumption = `(5x)/(6)"kg"`
Decrease in consumption
= `x - (5x)/(6)`
= `(x)/(6)`
Required % decrease in consumption
= `(x/6)/x xx 100`
= `(x)/(6x)xx 100`
= `(100)/(6)`
= `(50)/(3) = 16(2)/(3)`%
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