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### Question

Price of sugar is increased by 20%. By what percentage should consumption be reduced so that the expenditure remains same?

**A**

$16{2/3}$ %.

**B**

$26{1/2}$ %.

**C**

$15{2/3}$ %.

**D**

$11{4/5}$ %.

**Soln.**

**Ans: a**

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 20 = Rs. 120/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 120 × c, which gives c = 100/120, so the decrease is 1 - $100/120$ = ${120 - 100}/120$ × 100% = ${50/3}$, which is same as: $16{2/3}$%.