Question

30.
The price of sugar is increased by 25%. If the expenditure is not allowed to
increase, the ratio of the reduction in consumption to the original consumption is,
a) 5:1 b)1:5 c) 2:5 d) 3:5 e) cannot be determined​

Answer 1

Answer:

The correct option is b) 1:5

Explanation:

Consider the provided information.

Expenditure(E)= Price(p) x Consumption(c)

The price of sugar is increased by 25%

That means the price is now $\frac{125}{100}p$

But the expenditure is not allowed to  increase it means consumption should reduce, so that product of price and consumption will remains same.

Hence, to keep expenditure to be the same we can multiply cost by 100/125

$E=\frac{125}{100}p \times \frac{100}{125}c$

As we can see now the above equation is equivalent.

Now determine how much original Consumption decrease.

$\frac{100}{125}c=0.8c=80\%$

The consumption must go down by 20% in order for the expense to remain the same.

Now we need to determine the reduction in consumption to the original consumption,

$\frac{\text{Reduction in consumption}}{\text{Original consumption}} =\frac{20}{100}=\frac{1}{5}$

Hence, the required ratio is 1:5