Question

At Narmada Sarovar Bachao demonstration, supporters of Ms. Patkar outnumbered the police by $9:1$. The police arrested $135$ NSB supporters averaging $5$ for every $3$ police men. How many supporters of NSB were there in the demonstrations?

Answer 1

At first, we will try to find out the ratio between the number of NSB supporters who were arrested and the number of policemen. By using the total numbers of supporters and the above ratio we can find the number of policemen.
Then by the ratio between the supporters and police men we can find the total number of supporters who came for the demonstration.

Complete step-by-step answer: It is given that, at Narmada Sarovar Bachao demonstration, supporters of Ms. Patkar outnumbered the police by $9:1$.
Number of NSB supporters that the police arrested $135$.
It is also given that, $135$ NSB supporters were arrested averaging $5$ for every $3$ police men.
The number of policemen is found by multiplying number of NSB supporters arrested with$\dfrac{3}{5}$,
So, the number of police man $= 135 \times \dfrac{3}{5}$
Let us simplify the above equation to find the number of policemen,
On simplifying we get,
The number of policemen were $= 81$
Again, the ratio of the NSB supporters and the policemen was given as $9:1$
By multiplying $81$ with 9 we will find the number of NSB supporters as the ratio of NSB supporters and the policemen is $9:1$
So, the numbers of NSB supporters were $9 \times 81$
We simplify the above equation to get the required answer,
The numbers of NSB supporters were $729$.
Hence, there were $729$ NSB supporters for the demonstration.

Note: The statement ‘The police arrested $135$ NSB supporters averaging $5$ for every $3$ police men’ means that, every $5$ NSB supporters were arrested by $3$ police men.
So, the ratio between the NSB supporters that were arrested and the police men was $2:3$ .
The ratio of NSB supporters and the policemen is $9:1$that is there are 9 NSB supporters for 1 policeman.