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

Question

A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

(A) \(11x\)

(B) \(22x\)

(C) \(\frac{22x}{y}\)

(D) \(\frac{22x}{22-y}\)

(E) \(\frac{22x}{22xy-y}\)

(A)  11x

(B)  22x

(C)  \frac{22x}{y}

(D)  \frac{22x}{22-y}

(E)  \frac{22x}{22xy-y}

BrentGMATPrepNow · Accepted Answer

In a month with 22 working days, no units are produced in the first y working days because of a strike.  
Number of days in which units were produced = 22 - y
Let k = units produced each day in which units were produced 
So, TOTAL number of units produced in the month =  k(22 - y)

How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?   
We want: (total number of units produced)/(# of work days) = x
In other words, we want:  k(22 - y) /22 = x

We must solve the above equation for k

Take:  k(22 - y) /22 = x
Multiply both sides by 22 to get: k(22 - y) = 22x
Divide both sides by (22 - y) to get: k = 22x/(22 - y)

Answer: D

snehak93 · Answer

Simple:

Units  to be  produced(work to be done): 22x
Number of days no units were produced(time): y
Number of remaining working days(time): 22 - y

Work = Rate * Time 
Therefore Rate = Work/Time 
Rate = 22x/22-y

dave13 · Answer

say 10 units are produced each day

for whole month 220*10 = 220 units are produced

now if strike lasted for 11 working days

then 11x=220

x = 20

let x be number of units per day 10

let 22-y be number of days left after strike 11

SO JUST PLUG IN THOSE VALUES TO GET 20

clearly A, B, and E are out

Between C and D,

D is more logical i think

IMO: D

i wonder how would an algebraic solution look like GMATPrepNow

and how would you choose between D and C using my method of testing values - both yield the same value

ParthSanghavi · Answer

dave13

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.

ganand · Answer

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.

ParthSanghavi · Answer

Understood where i went wrong. Thank you :D

KanishkM · Answer

Plug in for all the unknown variables 
x = 10 units/day 
y = 5 
Remaining days 17

Average = Sum of the terms/ Total number of terms

whatever was lost in the 5 days needs to be recovered by working in the remaining days at a new rate
17 x = 220
x = 220/17

When plugged back for all the values, Only D gives us the same value

naveeng15 · Answer

say 10 units are produced each day

for whole month 220*10 = 220 units are produced

now if strike lasted for 11 working days

then 11x=220

x = 20

let x be number of units per day 10

let 22-y be number of days left after strike 11

SO JUST PLUG IN THOSE VALUES TO GET 20

clearly A, B, and E are out

Between C and D,

D is more logical i think

Confide · Answer

Let's not overcomplicate this question:
Total quantity produced in this month is 22x
because no units are produced in y days we have to subtract it from the total number of working days in this month to find how many units we have to produce in the remaining days
Units per day = Quantity/Total Days = 22x/22-y

simple as that (D) is correct

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

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