Tool By Zeal Point

Q. If the price of sugar increases by 20%, by what percentage should consumption be reduced so that the total expenditure remains the same ?

Solution

Suppose the original price of sugar = ₹100 per unit.

Price increases by 20%.

So, increase in price: $20% of 100 = ₹20$

Therefore, new price: $100 + 20 = ₹120$

Now, the total expenditure must remain the same.

So, if earlier we could buy 6 units at ₹100:

$Old expenditure = 6 \times 100 = ₹600$

At the new price of ₹120, with the same expenditure:

$New consumption = 600/120 = 5 units$

Therefore:

Percentage reduction is calculated on the original consumption:

$Reduction % = Reduction / Original Consumption \times 100$ $= 1/6 \times 100$ $= 16 2/3%$

Ans: 16⅔% decrease

Trick

If price increases by x%, then the required decrease in consumption is:

$x/100+x \times 100$

For 20% increase:

$20/120 \times 100$ $= 1/6 \times 100 = 16 2/3%$

Practice Question

If the price of sugar increases by 25%, by what percentage should consumption be reduced to keep the expenditure unchanged?

A) 15% B) 20% C) 25% D) 30%