Question 51

The number of students in a hostel increases from 5400 to 6075. By what percentage should the hostel reduce the per head consumption of food, so that the expenditure on food does not increase?

Solution

Let's assume the initial per head consumption of food is 'y'.

When students increased in the hostel, then the percentage reduction of the per head consumption of food is 'z'%.

The number of students in a hostel increases from 5400 to 6075. but the expenditure on food should not increase.

$$5400 \times y = 6075 \times y \times (100-z)%$$

$$8 = 9 \times (100-z)%$$

$$\frac{8}{9}=\frac{(100-z)}{100}$$

$$\frac{800}{9}=(100-z)$$
$$z=(100-\frac{800}{9})$$
$$z=\frac{900-800}{9}$$
$$z=\frac{100}{9}$$
$$z=11\frac{1}{9}$$%

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