Question

The students in three sections are in the ratio 2:3:5 if 12 students are increased in each section the ratio changes 4:5:7 what was the total number of students in the three sections before the increase

Answer 1

Let the total number of students be x.

Let the sections be A, B and C.

The ratios are :

2 : 3 : 5 respectively

The sum of the ratios is 2 + 3 + 5 = 10

The number of students in section :

A = 2/10x

B = 3/10x

C = 5/10x

When 12 students are added in each section we have :

A = 2/10x + 12

B = 3/10x + 12

C = 5/10x + 12

The new ratios of A : B : C is :

4 : 5 : 7

This is equal to :

(2/10x + 12) : (3/10x + 12) : (5/10x + 12) = 4 : 5 : 7

(2/10x + 12) : (3/10x + 12) = 4 : 5

(2/10x + 12) / (3/10x + 12) = 4/5

5{2/10x + 12} = 4{ 3/10x + 12}

x + 60 = 12/10x + 48

10x + 600 = 12x + 480

12x - 10x = 600 - 480

2x = 120

x = 60

The total number of students in the three sections before more students were added is thus 60