Question

The total number of pupils in three classes of a school is 333. The number of pupils in classes I and II are in the ratio 3:5 and those in
classes II and III are in the ratio 7:11. Find the number of pupils in the class that had the highest number of pupils.​

Answer 1

Answer:

class 3 has the highest number with 165 students

Step-by-step explanation:

hope explanation is comprehensive

in the step it is 23x+35x+55x=333

Answer 2

Class III had the highest number of pupils (165).

Given :

• The total number of pupils in three classes of a school is 333.

• The number of pupils in classes I and II are in the ratio 3 : 5 and those in classes II and III are in the ratio 7 : 11

To find :

The class which had highest number of pupils.

Solution :

Step 1 of 3 :

Find the ratio of number of pupils in three classes

Here it is given that number of pupils in classes I and II are in the ratio 3 : 5 and those in classes II and III are in the ratio 7 : 11

Class I : Class II = 3 : 5 = 21 : 35

Class II : Class III = 7 : 11 = 35 : 55

∴ Class I : Class II : Class III = 21 : 35 : 55

Step 2 of 3 :

Form the equation

Class I : Class II : Class III = 21 : 35 : 55

Let the number of pupils in Class I , Class II , Class III are 21x , 35x , 55x respectively

Now total number of pupils in three classes of a school is 333

By the given condition

$\displaystyle \sf{ 21x + 35x + 55x = 333 }$

Step 3 of 3 :

Find the class with highest number of pupils.

$\sf \: 21x + 35x + 55x = 333$

$\displaystyle \sf{ \implies 111x = 333}$

$\displaystyle \sf{ \implies x = \frac{333}{111} }$

$\displaystyle \sf{ \implies x = 3}$

Number of pupils in Class I = 21x = 21 × 3 = 63

Number of pupils in Class II = 35x = 35 × 3 = 105

Number of pupils in Class III = 55x = 55 × 3 = 165

Hence Class III had the highest number of pupils (165).

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