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 ${\displaystyle \frac{9}{5}}$ .
Number of drawings painted by 6 painters in one hour = ${\displaystyle \frac{9}{5}}$
So the number of drawings painted by 1 painter in 1 hour = ${\displaystyle \frac{9}{5\times 6}}={\displaystyle \frac{3}{10}}$
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 = ${\displaystyle \frac{3x}{10}}$
So number of drawings painted by x painters in 3 hours = ${\displaystyle \frac{3x}{10}}\times 3={\displaystyle \frac{9x}{10}}$
We have assumed x to be the number of painters required to make 9 drawings in 3 hours.
So we get
$\begin{array}{rl}& {\displaystyle \frac{9x}{10}}=9\\ & \Rightarrow {\displaystyle \frac{x}{10}}=1\\ & \Rightarrow x=10\end{array}$
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
$\begin{array}{rl}& {\displaystyle \frac{x}{6}}={\displaystyle \frac{5}{3}}\\ & \Rightarrow x={\displaystyle \frac{6\times 5}{3}}=10\end{array}$
So, 10 painters are required to paint 9 drawings in 3 hours.