Question

The price of sugar is increased by 20%. By what percent must the consumption of sugar be decreased so that the expenditure on sugar may remain the same?

Answer 1

Let price of x kg of sugar = Rs. 100

Increase in price = 20%

∴ New price = 100 + 20 = Rs.120

∴ For Rs. 120, sugar obtained = x kg.

For Rs. 100, sugar obtained

= `x/(120) xx 100`

= `(5x)/(6)"kg"`

Original consumption = x kg

New consumption = `(5x)/(6)"kg"`

Decrease in consumption 

= `x - (5x)/(6)`

= `(x)/(6)`

Required % decrease in consumption

= `(x/6)/x xx 100`

= `(x)/(6x)xx 100`

 = `(100)/(6)`

= `(50)/(3) = 16(2)/(3)`%

Answer 2

Assume initial values

Let the initial price of sugar = ₹100 per kg

Let the initial consumption = 1 kg

Expenditure = Price × Quantity = 100 × 1 = ₹100

Price increases by 20% → New price = 100 + 20 = ₹120 per kg

`"New consumption" = "Expenditure"/"New Price" = 100/120 = 5/6 kg`

Old consumption = 1 kg

New consumption = 5/6 kg

Decrease in consumption = `1 - 5/6 = 1/6`

Percentage decrease = `1/6/1 xx 100 = 16 2/3 %`