Question

12 painters can paint a wall of 180 m long in 3 days. How many painters are required to paint 200 m long wall in 5 days?

Answer 1

Let the number of painters be $x$.
Now, number of painters$\left(p_1\right)$ ∝ length of the wall$(l_1$)
number of painters$\left(p_1\right)$ ∝ $\frac{1}{\text{Number of days}{(d}_1)}$

⇒ $p_1$ ∝ $\frac{l_1}{d_1}$
⇒ $\frac{p_1{d}_1}{l_1}=\text{constant}$

∴ $\frac{p_1{d}_1}{l_1}=\frac{p_2{d}_2}{l_2}$

Here, $p_1=12$, $d_1=3$, $l_1=180$, $p_2=x$, $d_2=5$, $l_2=200$

⇒$\frac{12\times 3}{180}=\frac{x\times 5}{200}$
⇒ $x=\frac{12\times 3\times 200}{180\times 5}=8$

Hence, 8 painters will be required to build 200 m long wall in 5 days. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->