15. X number of men can finish a piece of work in 30
days. If there were 6 men more, the work could be
finished in 10 days less. What is the original number
of men?
(a) 10
(b) 11 (c) 12 (d) 15
(e) 13
Answers
Required Answer:-
Firstly,
- Let's understand the relation between the number of men and number of days for doing a piece of work.
- If there were less number of men, more days will be required to complete the work.
- They are indirectly proportional to each other. It means, if number of men = x, number of days = m. Then x1.m1 = x2.m2
Now, Let's come to the question.
X men take 30 days to complete a work.
1 men will takes 30 × X days to complete then. (From the above relation).
And,
If there were 6 more men, then number of men now is X + 6. No. of days is 30 - 10 = 20 days.
X + 6 men take 20 days to complete.
1 men will take (X + 6)20 days then..
That means,
⇒ 30X = (X + 6)20
⇒ 30X = 20X + 120
⇒ 10X = 120
⇒ X = 12 men
Initially,
The no. of men were X i.e. 12 (Option C)
Answer:
X number of men can finish a piece of work in 30 days. ==> Total work = 30X Men days. -- (1)
X number of men can finish a piece of work in 30 days. ==> Total work = 30X Men days. -- (1)If there were 6 men more, the work could be finished in 10 days less. ==> Total work = (X+6)*20 days -- (2)
X number of men can finish a piece of work in 30 days. ==> Total work = 30X Men days. -- (1)If there were 6 men more, the work could be finished in 10 days less. ==> Total work = (X+6)*20 days -- (2)By (1) and (2) we have:
X number of men can finish a piece of work in 30 days. ==> Total work = 30X Men days. -- (1)If there were 6 men more, the work could be finished in 10 days less. ==> Total work = (X+6)*20 days -- (2)By (1) and (2) we have:30X = (X+6)*20 => 10X = 120 => X = 12 men.