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 da

2 thoughts on “15. X number of men can finish a piece of work in 30<br />days. If there were 6 men more, the work could be<br />finished in 10 da”

1. 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 [tex] \times [/tex] x = 20(6 + x)

   30x = 120 + 20x

   30x – 20x = 120

   10x = 120

   x = 120/10

   x = 12

   [tex]\\[/tex]

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2. 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[tex].[/tex]

   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)

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