15 persons begin to work together on a job, but after some days 6 persons leave. As a result, the job which could have been completed in 42 days is completed in 54 days. After how many days of the commencement of the work did 6 persons leave?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 24
Given:
15 persons begin to work together on a job, but after some days 6 persons leave.
As a result, the job which could have been completed in 42 days is completed in 54 days
Formula used:
Total work = Efficiency × time × persons ---- (1)
Calculations:
Let the efficiency of each person be x and after y days 6 persons left the job
Using equation (1),
Total work = 15 × x × 42 = 630x units
Remaining persons = 15 - 6 = 9
Remaining work = 630x - (15 × x × y)
Days 9 persons worked = (54 - y)
According to the question;
⇒ 630x - (15xy) = 9 × x × (54 - y)
Divide the whole equation above by x
⇒ 630 - 15y = 9 × (54 - y)
⇒ 630 - 15y = 486 - 9y
⇒ 630 - 486 = 15y - 9y
⇒ 144 = 6y
⇒ y = 24