Question

due to increase in the price of sugsr by 25%,by how much percent must a householder decrease the consumption of sugar so that there is no increase in the expenditure on sugar?

Answer 1

As you know,
Price x Consumption = Expenditure.

So, for the expenditure to remain constant, when 1 quantity increases the other quantity should decrease proportionally. 
Say, for eg: the expenditure for a householder is Rs. 100
Initial price of sugar per kg = Rs. 20
Hence, initial consumption (quantity) = 100/20 = 5 kg
Now, the expenditure is same = Rs.100
Increase in price of sugar = 20 + 25% of 20 = 20 x 125/100 = Rs.25
Hence, consumption (quantity) = 100/25 = 4 kg.

So, when the sugar price increased by 25% , his consumption decreased from 5 kg to 4 kg
% decrease in consumption = (5-4)/5 x 100 = 20%

So, to maintain the expenditure when the price of sugar increases by 25%, one should decrease the consumption by 20%.
OR (Ratio method)

Price is 'inversly proportional' to consumption
Increase in price = 25%
25% = 25/100 = 1/4.....4(initial price)=== 5(final price)

Since, consumption is inversly proportional:
              Consumption: 5(initial)====== 4(final)
Hence % decrease = (5-4)/5 x 100 = 20%
[Check: Initial price x initial consumption = 4x5 = 20... Final price x final consumption = 5 x 4 = 20.. Expenditure remains constant]
Hope it helps

Answer 2

Let amount of the sugar = 100kg
Let the price of sugar be = ₹100

Therefore, increased price = ₹100 + ₹25 = ₹125

So, now ₹125 can fetch 100 kg.

Therefore,
Sugar which can be bought in ₹100 = 100/125*100 = 80
[100-80]%
= 20%

Answer:- The householder must decrease his consumption by 20%.

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