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.
ParthSanghaviQuote:
Below is my working. Could let me know where i made a mistake?
Total Units per Month = 22x.
No. of units lost due to strike of y days = xy.
No. of units to be produced in the remainder of the month= 22x+xy
No. of days left in the month after strike y = 22-y.
Hence, per day rate= 22x+xy/ 22-y
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.