Question

If 55% of the teachers in a school are gents and the number of lady teachers in the school is 90, then the total number of teachers in the school is:

Answer 1

Hint: Let total number of teachers in the school as a, total number of Male teachers as b and total number of Female teachers given as 90
Now we are given that 55% of the teachers in a school are gents so it means 45% of teachers are female teachers
So, we can write it as \[\dfrac{45}{100}\times a=90\] and finding the value of a

Complete step-by-step answer:
Assuming total number of teachers in the school as a, total number of Male teachers as b and total number of Female teachers is given as 90
One thing we know that Total no of teachers is formed by sum of male teachers and female teachers So if we are given 55% of the total teachers in a school are gents, it means percentage of female teachers in school are 45%
\[100%-55%=45%\]
Now we got that 45% of total teachers are female teachers
We know that x% of any number means that x multiply by that number divide by 100
So, 45% of total teachers are female teachers, we can write this as
\[\dfrac{45}{100}\times a=90....(1)\] in mathematical form
Here value of x is 45, that number is a and total female teachers are given a 90
After solving we got the value of a as 200
We can also calculate no of male teachers by using
\[\dfrac{55}{100}\times a=b....(2)\] , we are given that 55% of total teachers are male teachers
Putting a=200 in equation (2)
\[\dfrac{55}{100}\times 200=b\]
b=110
We can check that sum of female and male teachers make it to total number of teachers
\[b+90=200...(3)\]
 where we have calculated b=110 putting it to equation (3) it satisfies
Hence total number of teachers are 200

Note: We can also do it by another method that is we know that total teachers is a and can be written as \[b+90=a\] now we have given that 55% of the total teachers in a school are gents
So, it can be written as \[\begin{align}
  & \dfrac{55}{100}\times a=b \\
 & \\
\end{align}\] now putting value of b in equation \[b+90=a\]
It can be written as \[\begin{align}
  & \dfrac{55}{100}\times a+90=a \\
 & \\
\end{align}\] on solving can be written as \[\begin{align}
  & 90=a(1-\dfrac{55}{100}) \\
 & \\
\end{align}\]
And solve it and got an equal to 200