Question

3workers transfer a tool weginig 120 kg in 12 second how many men are required to transfer it in 9 seconds

Answer 1

4 workers are required to transfer the tool in 9 seconds.

Unitary method:

Mathematically, the problem is

$\underline{time\:(seconds)}\:\:\: \underline {number\:of\:men}\\ 12\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:3\\ 9\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:?$

Using unitary method, we can write

12 seconds time is taken by 3 workers

∴ 1 second time will be taken by (3 × 12) = 36 workers

∴ 9 seconds time will be taken by (36 ÷ 9) = 4 workers

Therefore, 4 workers are required to transfer the tool in 9 seconds.

Proportion method:

Mathematically, the problem is

$\underline{time\:(seconds)}\:\:\: \underline {number\:of\:men}\\ 12\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:3\\ 9\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:?$

Here, time and number of men are in inverse proportion.

Then, 9 : 12 :: 3 : x

$\Rightarrow \dfrac{9}{12}=\dfrac{3}{x}$

$\Rightarrow x=\dfrac{3\times 12}{9}$

$\Rightarrow x=\dfrac{36}{9}$

⇒ x = 4

Therefore, 4 workers are required to transfer the tool in 9 seconds.