A factory normally produces x units per working day. In a month with 2

Hi,

Given:

A factory normally produces x units per working day. In a month with 22 working days, no. of units required to be produced = 22*x units.

No units are produced in the first y working days because of a strike. => No. of working days reduced to (22 - y) days.

Now, the factory has to produce 22x units in (22-y) days. Hence, new average \(= \frac{22x}{22 - y}\).

DAVE:

This is very much possible that with a particular set of values more than one option might be true. In such cases, you have to recheck the answer with another set of values.

For example, now consider x = 10, and y = 2. => In 22-y = 20 days factory has to produce 220 units => average = 220/20 = 11 units/day.

(C) 22x/y => (22*10)/2 = 110 units. OUT

(D) 22x/(22-y) => (22*10)/20 = 11 units. Option (D) matches, hence right answer.

ParthSanghavi



Total production is fixed. Total units in a month = 22x. Hence, no. of units to be produced in a month will also be 22x.

Alternate Solution:

Old average = x units days.

No. of units lost due to strike = x*y units. These x*y units have to be produced on the remaining 22-y days.

No. of remaining working days = 22-y days.

New average \(= x + \frac{xy}{22 - y} = \frac{x*(22 - y) + xy}{22 - y} = \frac{ 22x - xy + xy}{22 - y} = \frac{22x}{22 -y}\).

Hope this helps.

Thanks.