Question

The students in three classes are in the ratio 2: 3: 5. If 20 students are increased in each class, the ratio changes to 4: 5: 7. The total number of students before the increases was - select one: a. 100 b. 10 c. 90 d. None of these

Answer 1

Given, ratio of students in three classes is 2 : 3 : 5

So, let the number of students in each class be 2x, 3x and 5x

If 20 students increased in each class, the students in three classes becomes 2x + 20, 3x + 20 and 5x + 20

After increasing the number of students in each class, the ratio of students becomes 4 : 5 : 7 i.e 4x, 5x and 7x



According to the question,

2x + 20 + 3x + 20 + 5x + 20 = 4x + 5x + 7x

➾ 10x + 60 = 16x

➾ 60 = 16x - 10x

➾ 60 = 6x

➾ $\dfrac{60}{6}$ = x

➾ 10 = x



No. of students in 1st class before incresing ➾ 2x

➾ 2 × 10

➾ $\underline{20}$

No. of students in 2nd class before increasing ➾ 3x

➾ 3 × 10

➾ $\underline{30}$

No. of students in 3rd class before increasing ➾ 5x

➾ 5 × 10

➾ $\underline{50}$



Total number of students ➾ 20 + 30 + 50

➾ $\boxed{100}$





∴ The number of students in 1st, 2nd and 3rd classes are 20, 30 and 50 respectively and total is 100

Answer 2

Solutions :-

Let the the ratio 2: 3: 5 be 2x, 3x and 5x respectively.

Let the changed ratio 4: 5: 7 be 4x, 5x and 7x respectively.

According to the question,

=> 2x + 20 + 3x + 20 + 5x + 20 = 4x + 5x + 7x
=> 10x + 60 = 16x
=> 10x - 16x = - 60
=> - 6x = - 60
=> x = -60/-6 = 10

Now,
The total number of students before the increases was :-

2x + 3x + 5x = (2 × 10) + (3 × 10) + (5 × 10)
= 100


Answer : option (a) 100 is the required answer.