ANSWER
![\frac{7}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B10%7D%20)
EXPLANATION
It was given that, 10 people can paint a building in 5days.
We can write the ratio,
![10 : 1](https://tex.z-dn.net/?f=10%20%3A%201)
Now we want to find how much of the building
7 people could paint in the same 5 days working at the same rate.
Let it be in the ratio,
![7 : x](https://tex.z-dn.net/?f=7%20%3A%20x)
Then we can write and solve the following proportional equation for x,
![10 : 1 = 7 : x](https://tex.z-dn.net/?f=10%20%3A%201%20%3D%207%20%3A%20x)
We can rewrite this as a fraction to get,
![\frac{10}{1} = \frac{7}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B1%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7Bx%7D%20)
Let us now cross multiply to get,
![10x = 7](https://tex.z-dn.net/?f=10x%20%3D%207)
We divide both sides by 10 to obtain,
![x = \frac{7}{10}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B7%7D%7B10%7D%20)
This means the 7 people can only paint a fraction ( 70%) of the building and not the whole building.