correct answer is: b) 100 metres

Explanation

9 frocks made by a tailor out of 12 metres of cloth
\therefore 1 frocks made by a tailor out of \large\frac{12}{9} metres of cloths
\therefore 75 frocks made by a tailor out of \large\left(\frac{12\times75}{9}\right) metres of cloths
\rightarrow 100 metres of cloths
Ans: 100 metres of cloths should a tailor buy to make 75 frocks.

Another way, Rules of Three Method

Frocks and Cloths are Directly Proportional.
\therefore\;9\;:\;75\;:\;:\;12\;:\;x
\rightarrow\large\frac{9}{75}=\frac{12}{x}
\rightarrow 9x=75\times12
\rightarrow x=\large\frac{75\times12}{9}
\rightarrow x=100
Ans: 100 metres of cloths should a tailor buy to make 75 frocks.

Other ways to ask this same math question are:

1. If a tailor can make 9 frocks out of 12 meters of cloth, how much cloth should he buy to make 75 frocks?
2. How many meters of cloth does a tailor need to buy to make 75 frocks if he typically makes 9 frocks out of 12 meters of cloth?
3. Given that a tailor can produce 9 frocks using 12 meters of cloth, how many meters of cloth will be required for him to make 75 frocks?
4. If a tailor typically makes 9 frocks out of 12 meters of cloth, how much cloth should he purchase to make 75 frocks?
5. Suppose a tailor uses 12 meters of cloth to make 9 frocks. How many meters of cloth does he need to make 75 frocks?