SSC CHSL 2024 PYQ — Question 75

The correct answer is option 3 i.e.  Decrease $12 \frac{1}{2}\%$ .

Short method:

The cost of rice is increased by 25% but its consumption is decreased by 30%

Percentage change = x + y + xy/100

= 25 - 30 - (25 × 30)/100

= -5 - 7.5 = -12.5%  

= $12 \frac{1}{2}\%$ Decrease 

Alternate method:

The initial cost of rice = ( C ) per unit

The initial quantity consumed = ( Q).

Initial Expenditure = C × Q

New Cost = C + 0.25C = 1.25C

New Quantity = Q - 0.30Q = 0.70Q

New Expenditure = 1.25C ×  0.70Q = 0.875C × Q

Percentage Change = New Expenditure - Initial Expenditure / Initial Expenditure ×  100

Percentage Change = $\frac{0.875C \times Q - C \times Q}{C \times Q} \times 100$

Percentage Change = $\frac{(0.875 - 1)C \times Q}{C \times Q} \times 100$

Percentage Change = $\frac{-0.125C \times Q}{C \times Q} \times 100$

Percentage Change = -12.5%