# If 6 painters can complete 9 drawings in 5 hours then How many painters will make 18 drawings in 5 hours?

A) 11

B) 12

C) 13

D) 14

Answer

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**Hint:**

We can take x as the number of painters that will complete 18 drawings in 5 hours. Then we can estimate the amount of drawing completed by one painter in one hour by dividing the given number of paintings with the number of painters and number of hours. Then we can find the part of drawing completed by x painters in 5 hours by multiplication. Then we can equate this with 18. Then we can solve for x to get the required number of painters.

**Complete step by step solution:**

It is given that 6 painters can complete 9 drawings in 5 hours.

We can write it as amount of drawing 6 painters completed in 5 hours is 9

Now we can find the part of drawing 6 painters complete in 1 hour. It is obtained by dividing the above value with 5.

The part of drawing 6 painters completed in 1 hour \[ = \dfrac{9}{5}\] .

Now we need to find the amount of drawing completed by 1 painter in 1 hour. It can be found out by dividing the above value with the number of painters which is 6.

Therefore, the part of drawing 1 painter completed in 1 hour $ = \dfrac{9}{{5 \times 6}}$ .

Let the number of painters that will make 18 drawings in 5 hours be x. Then we can find the amount of drawing completed by x painters in 1 hour.

Therefore, the part of drawing x painter completed in 1 hour $ = \dfrac{9}{{5 \times 6}}x$ .

Now we can find the part of drawing completed by x painters in 5 hours. It can be found by multiplying the above equation with 5.

So, the amount of drawing x painters completed in 5 hours $ = \dfrac{{9 \times 5}}{{5 \times 6}}x$ .

It is given that x painters complete 18 drawings in 5 hours. So, we can equate the above value to 18.

$ \Rightarrow 18 = \dfrac{{9 \times 5}}{{5 \times 6}}x$

On rearranging, we get,

$ \Rightarrow x = \dfrac{{6 \times 5 \times 18}}{{5 \times 9}}$

On cancelling the common factors, we get,

$ \Rightarrow x = 6 \times 2$

$ \Rightarrow x = 12$

Therefore, 12 painters will make 18 drawings in 5 hours.

**So, the correct answer is option B.**

**Note:**

Alternate solution to solve this problem is,

As the number of hours is the same in both the cases, we can take the proportionality.

Let the number of painters that will make 18 drawings in 5 hours be x.

Then by proportionality, we can write,

\[\dfrac{x}{{18}} = \dfrac{6}{9}\]

On rearranging, we get,

\[ \Rightarrow x = \dfrac{{6 \times 18}}{9}\]

On further simplification, we get,

$ \Rightarrow x = 12$

Therefore, 12 painters will make 18 drawings in 5 hours.

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