Price of a commodity has increased by 60% by what per cent must a consumer reduce the consumption of the commodity so as not to increase the expenditure?a)47b)37.5c)30.5d)50Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Solution:

Let the initial price of the commodity be Rs. 100 and initial consumption be x units.

After the price hike of 60%, the new price of the commodity = Rs. 100 + (60/100)*100 = Rs. 160

Let the consumer reduce the consumption by y%.

Then, the new expenditure = Rs. (100-y)/100 * 160 * x

We need to find the value of y such that the new expenditure is equal to the initial expenditure.

Initial expenditure = Rs. 100*x

Therefore, (100-y)/100 * 160 * x = 100*x

Simplifying, we get:

160(100-y) = 100*100

16000 - 160y = 10000

160y = 6000

y = 6000/160 = 37.5%

Hence, the consumer must reduce the consumption of the commodity by 37.5% so as not to increase the expenditure.

Therefore, option (b) is the correct answer.

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