Question

If 6 painters can paint 9 drawings in 5 hours then find the number of painters required to paint 9 drawings in 3 hours.
(a) 5
(b) 10
(c) 12
(d) 15

Answer 1

Hint: First calculate the contribution of each painter in one hour. Then you can easily get the number of painters required to paint 9 drawings in 5 hours. It is a question of time and work so apply concepts related to it.

Complete step-by-step answer:

It is given that 6 painters can paint 9 drawings in 5 hours. So the number of drawings they can do in one hour is $\dfrac{9}{5}$ .
Number of drawings painted by 6 painters in one hour = $\dfrac{9}{5}$
So the number of drawings painted by 1 painter in 1 hour = $\dfrac{9}{5\times 6}=\dfrac{3}{10}$
Let x be the number of painters required to paint 9 drawings in 3 hours.
Then the number of drawings which can be painted by x painters in 1 hour can be calculated using the contribution of each painter in 1 hour.
Number of drawings painted by x painters in 1 hour = $\dfrac{3x}{10}$
So number of drawings painted by x painters in 3 hours = $\dfrac{3x}{10}\times 3=\dfrac{9x}{10}$
We have assumed x to be the number of painters required to make 9 drawings in 3 hours.
So we get
$\begin{align}
  & \dfrac{9x}{10}=9 \\
 & \Rightarrow \dfrac{x}{10}=1 \\
 & \Rightarrow x=10 \\
\end{align}$
So, 10 painters are required to paint 9 drawings in 3 hours.

Note: There is one shortcut way to solve this question. Since the number of drawings is the same in both cases, only the duration of paint is changed, we can apply a ratio proportion between number of painters and time taken to complete the work (9 paintings).
Number painter is inversely proportional to time given for painting.
Let x denote the number of painters required to paint 9 drawings in 3 hours, then we have
$\begin{align}
  & \dfrac{x}{6}=\dfrac{5}{3} \\
 & \Rightarrow x=\dfrac{6\times 5}{3}=10 \\
\end{align}$
So, 10 painters are required to paint 9 drawings in 3 hours.