Question

The price of sugar goes up by 20%. By how much per cent must a housewife reduce her consumption of sugar so that the expenditure on sugar remains the same?​

Answer 1

Step-by-step explanation:

let the price of 1kg sugar be Rs x

if if the price of sugar goes up by 20% then let the new price be Rs x + 20/100 (x)

= x+x/5

=6x/5

Now the housewife has to buy sugar worth rupees x only. therefore she has to reduce the amount of sugar she has bought.

the price is 6x/5 for 1kg sugar

price of rupees x is 1/6x *5x = 5/6 kg

therefore reduction in percentage is (1-5/6) =1/6

therefore percent that the house wife you must reduce consumption =

(1/6)/1 × 100%

16.67%

Answer 2

Step-by-step explanation:

Let the price of 100 kg of sugar be originally be ₹100.

After increment of price

Cost of 100 kg of sugar= ₹(100+20)=₹120.

Now,

$₹120 \: yields \: 100kg \: of \: sugar \\ ₹100 \: yields \: ( \frac{100}{120} \times 100)kg \: of \: sugar \\ i.e. \frac{250}{3} kg$

So,

$reduction \: in \: consumption = (100 - \frac{250}{3} )\%= \frac{50}{3}\% = 16 \ \frac{2}{3} \%$