Question

10 workers complete a piece of work in 30 days. i)In how many days would 1 worker complete the work? Ii}In how many days would 15 workers complete the same work?

Answer 1

Proportion

We know that :

If the number of workers ( W ) 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 workers is inversely proportional to number of days.

⇒ W ∝ 1 / D

⇒ W × D = Constant

⇒ W₁D₁ = W₂D₂

Case 1 :

10 workers complete a piece of work in 30 days. Number of days taken to complete by 1 worker = ?

Here :

• W₁ = 10
• D₁ = 30
• W₂ = 1
• D₂ = ?

Now using the formula as we I have mentioned above

⇒ W₁D₁ = W₂D₂

⇒ 10 × 30 = 1 × D₂

⇒ 300 = D₂

⇒ D₂ = 300

Therefore 1 worker can complete the same work in 300 days.

Case 2 :

10 workers complete a piece of work in 30 days. Number of days taken to complete by 15 workers = ?

Here :

• W₁ = 10
• D₁ = 30
• W₂ = 15
• D₂ = ?

Now using the formula as we I have mentioned above

⇒ W₁D₁ = W₂D₂

⇒ 10 × 30 = 15 × D₂

⇒ 300/15 = D₂

⇒ D₂ = 20

Therefore 15 workers can complete the same work in 20 days.