Question

Three persons working 3 hours a day assemble 3 machines in three days. The number of machine assembled by 4 persons working 4 hours a day in 9 days is

Answer 1

Answer: 48 machines

Step-by-step explanation:

Since, if $x_1$, person do $w_1$ work in $n_1$ days working $h_1$ hours per day while $x_2$, person do $w_2$ work in $n_2$ days working $h_2$ hours per day,

Then,

$\frac{x_1\times n_1\times h_1}{w_1}=\frac{x_2\times n_2\times h_2}{w_1}$

Here, $x_1=3$, $n_1$=1, $h_1$=3, $w_1$ = 3, $x_2$= 4, $n_2$ = 9, $h_2$=4, $w_2$= ?

⇒ $\frac{3\times 1\times 3}{3}=\frac{4\times 4\times 9}{w_2}$

⇒ $\frac{9}{3}=\frac{144}{w_2}$

⇒ $9w_2=432$

⇒ $w_2=48$

Answer 2

Answer:

8

Step-by-step explanation:

Given : Three persons working 3 hours a day assemble 3 machines in three days.

To Find :No. of machine assembled by 4 persons working 4 hours a day in 9 days

Solution:

Let $x_1$ and $x_2$denotes the no. of people working in both cases respectively.

Let $w_1$ and $w_2$denotes work done in both cases respectively.

Let $h_1$ and $h_2$denotes no. of hours work done in both cases respectively.

Let $d_1$ and $d_2$denotes no. of days work done in both cases respectively.

So, $x_1=3\\w_1=3\\h_1=3\\d_1=3\\x_2=4\\h_2=4\\d_2=9$

Formula : $\frac{x_1 \times d_1 \times h_1}{w_1}=\frac{x_2 \times d_2 \times h_2}{w_2}$

$\frac{3 \times 3 \times 3}{3}=\frac{4 \times 9 \times 2}{w_2}$

$w_2=\frac{4 \times 9 \times 2}{3 \times 3 \times 3} \times 3$

$w_2=8$

Hence 8  machine assembled by 4 persons working 4 hours a day in 9 days