A group of men decided to do a job in 5 days, but 10 men kept dropping out every day. If the job was completed at the end of the 6th day, find the initial number of men who had signed up for the work.
120
150
160
180
Answers
Answer:A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning?
A. 240
B. 140
C. 280
D. 150
E. None of these
Answer: Option B
Solution
Let X be the initial number of men then,
According to the question,
4X = X + (X - 20) + (X - 40) + (X - 60) + (X - 80) + (X - 100) + (X - 120)
⇒ 4X = 7X - 420
⇒ 3X = 420
⇒ X = 4203
⇒ X = 140 men
Step-by-step explanation:
Given : A group of men decided to do a job in 5 days, but 10 men kept dropping out every day . job was completed at the end of the 6th day
To Find : the initial number of men who had signed up for the work.
Solution:
Let say number of men = M
Total work = M*5 Man days
Man worked on 1st day = M
Work done on 1st day = M Man day
Work done on 2nd day = M-10 Man day
Work done on 3rd day = M-20 Man day
Work done on 4th day = M-30 Man day
Work done on 5th day = M-40 Man day
Work done on 6th day = M-50 Man day
Total work done = M + M - 10 + M - 20 + M - 30+ M - 40 + M - 50
= 6M - 150 man days
6M - 150 = 5M
=> M = 150
Initial number of men who had signed up for the work.= 150
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