Question

If 1 pint is needed to paint a statue 6 m high, then the number of pints it will take to paint(to the same thickness) 540 statues similar to the original but only 1 m high is-
A. 90
B. 72
C. 45
D. 15

Answer 1

Hint:We will use the unitary method in this problem. We will start by finding the amount of paint(in pints) required to paint one metre of the bigger statue. Then we will find the total height of the 540 statues. FInally, we will multiply the amount of paint per metre by the total length, which will give us the total amount of paint required.

Complete step-by-step answer:
We have been given that 1 pint of paint is required to paint a statue 6 m high. So, we will find the amount of paint required to paint 1 m of the same large statue. This can be obtained by dividing the total amount of paint used by the total height as-
 $ \dfrac{{Total\;Amount}}{{Total\;Height}} = \dfrac{1}{6} $ pints/metre…(1)
Now, we will find the total length of the 540 statues in metres which will give us the amount to be painted. This can be calculated by multiplying the number of statues by the length of each statue, which can be done as-
 $ Total\;statues \times Height\;of\;small\;statue = 540 \times 1 = 540\;{\text{m}} $ ...(2)
Finally, we now have the total length required to be painted and the amount of paint required to paint one meter. To find the total amount of the paint, we will multiply these two quantities obtained in equations (1) and (2) as-
 $ Total\;paint = \dfrac{1}{6} \times 540 = 90\;pints $

This is the total amount of paint required to paint the 540 smaller statues. The correct option is A.

Note: An important point to note here is that an assumption has been made which states that the thickness of the paint is the same on all the statues, hence we can directly apply the unitary method without worrying about the paint. Also, students in a hurry often forget the fact that the 540 statues are 1 m in height only, and they assume that the height of all the statues is 6 m each.