The price of onions increases by 25%, by what percent should a housewife reduces theconsumption so that expenditure on onions can be same as before?a)25%b)30%c)20%d)40%Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
The price of onions increases by 25%.

To find:
By what percent should a housewife reduce the consumption so that the expenditure on onions can be the same as before?

Solution:

Let's assume the initial price of onions per unit is P and the initial consumption is C. Therefore, the initial expenditure on onions is given by E = P * C.

After a 25% increase in price, the new price per unit of onions becomes P + 0.25P = 1.25P.

Let's assume the new consumption is x. Therefore, the new expenditure on onions is given by E' = (1.25P) * x.

Since we want the expenditure to be the same as before, we can equate E and E':

E = E'
P * C = (1.25P) * x

Finding the reduction in consumption:
To find the reduction in consumption, we need to calculate the difference between the initial consumption and the new consumption, and express it as a percentage of the initial consumption.

Let's substitute the value of P * C from equation (1) into equation (2):

P * C = (1.25P) * x
C = 1.25x

The reduction in consumption is given by (C - x), and we need to find this as a percentage of the initial consumption (C).

Reduction in consumption = (C - x)
Percentage reduction = ((C - x) / C) * 100

Substituting the value of C = 1.25x, we have:

Percentage reduction = ((1.25x - x) / (1.25x)) * 100
Percentage reduction = (0.25x / 1.25x) * 100
Percentage reduction = (0.25 / 1.25) * 100
Percentage reduction = 20%

Therefore, the housewife should reduce the consumption by 20% so that the expenditure on onions remains the same as before.

Answer:
Option c) 20%

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