Question

7) Ii a certain examination , the number of those who passed was 4 tmes the

number of those who failed. If there had been 35 fewer caididates and 9 more

had failed, the ratio of the passed and failed caididates would have been 2 : 1.

The total number of caididates who appeared ii the examination was​

Answer 1

Working out:

In the question, we are provided with some conditions and relations between the passed and failed students.

GiveN:-

• Number of passed students is 4 times the number of failed students.
• If there had been 35 less students and 9 more failed, then ratio of passed : failed = 2 : 1

We have to find the total number of students who appeared in the examination.

Let,

• Number of failed students be x
• Then, Number of passed students be 4x

Then total number of students = x + 4x = 5x

According to the given condition,

• 35 less than total students = 5x - 35
• 9 more failed students = x + 9

Then the number of passed students:

$\sf{ \longrightarrow{5x - 35 - (x + 9)}}$

$\sf{ \longrightarrow{5x - 35 - x - 9}}$

$\sf{ \longrightarrow{4x - 44}}$

Now it is given that,

• Ratio of passed to failed students = 2 : 1

So,

$\sf{ \longrightarrow{ \dfrac{4x - 44}{x + 9} = \dfrac{2}{1} }}$

Cross multiplying,

$\sf{ \longrightarrow{4x - 44 = 2(x + 9)}}$

$\sf{ \longrightarrow{4x - 44 = 2x + 18}}$

Since we need to find x, So let's isolate x to one of the side.

$\sf{ \longrightarrow{4x - 2x = 18 + 44}}$

$\sf{ \longrightarrow{2x = 62}}$

$\sf{ \longrightarrow{x = \dfrac{62}{2} = 31}}$

So, The number of passed and failed students:

• No. of passed students = 4x = 124
• No. of failed students = x = 31

Total number of students:

$\huge{ \boxed{ \sf{ \red{5x = 155}}}}$

And we are done !!