Q12 of 20 Page 111

The price of sugar has increased by 20%. Let’s work out the percentage of decrease in consumption of sugar if the monthly expenses of sugar remain same.

Given: The percentage increment in the price of sugar=20%.


Tip:(i) if y is increased by x% then the new value of y is



(ii)


In the given question, neither the price of a single unit of sugar is written nor the quantity that is consumed daily is mentioned but the monthly cost of sugar is constant, and this is our hint and we will use this in the form of an equation.


(Actually, the price and quantity are not mentioned since percentage calculation of decrement is independent of these terms as we will see.)


Let us assume the price of a single unit of sugar be Rs. y.


Let us assume the quantity of sugar intake per month before price hike be x.


Therefore, monthly expenditure is Rs.


Now, using tip (i)


The new price of sugar is Rs.



Let the new quantity of sugar intake per month i.e; reduced intake be z.


But, in the question, it is given that the monthly expenditure both before and after price hike should be the same.


Therefore, we can write


The new price of sugar Reduced intake of sugar=previous monthly


expenditure on sugar


or,



or,



Therefore, the decrement in sugar intake=x-z




Now, using tip(ii)


The decrement percentage is





=16.667%


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