Question

3.6 men can do a piece of work in 12 days.
i) In how many days would 1 man do the
same work?
ii)In how many days would 8 men do the
same work?

Answer 1

Proportion

We know that :

If the number of men ( M ) increases to do a piece of work then at the same time number of days ( D ) taken to complete the work will decrease.

Hence, number of men is inversely proportional to number of days.

⇒ M ∝ 1 / D

⇒ M × D = Constant

⇒ M₁D₁ = M₂D₂

Case 1 :

6 men can do a piece of work in 12 days. Number of days taken by 1 man = ?

Here :

• M₁ = 6
• D₁ = 12
• M₂ = 1
• D₂ = ?

Now using the formula given above

⇒ M₁D₁ = M₂D₂

⇒ 6 × 12 = 1 × D₂

⇒ 72 = D₂

Therefore 1 man can do the same work in 72 days.

Case 2 :

6 men can do a piece of work in 12 days. Number of days taken by 8 men = ?

Here :

• M₁ = 6
• D₁ = 12
• M₂ = 8
• D₂ = ?

Now using the formula given above

⇒ M₁D₁ = M₂D₂

⇒ 6 × 12 = 8 × D₂

⇒ 72/8 = D₂

⇒ D₂ = 9

Therefore 8 men can do the same work in 9 days.