Question

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​

Answer 1

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 2

Given:-

If . 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.

To Find :-

What is the original number  of men?

Solution :-

We may observe that the question is going in indirect proportion

Here,

30 $\times$ x = 20(6 + x)

30x = 120 + 20x

30x - 20x = 120

10x = 120

x = 120/10

x = 12