Question

The students in the three hostels are in a ratio of 2 : 3 : 5. If the students are increased by 5 in each hostel, the new ratio will become 5 : 7 : 11. The total number of students in the three hostels after the increase is?

1. 120
2. 110
3. 115
4. 130
5. 100

Answer 1

Correct Answer - Option 3 : 115

Given:

Initial ratio of students in the hostel = 2 : 3 : 5

New ratio of students in the hostel = 5 : 7 : 11

Concept used:

Initial value + Increment = Final value

Calculation:

Let the number of students in the first hostel be 2x

Let the number of students in the second hostel be 3x

Let the number of students in the third hostel be 5x

(2x + 5)/(3x + 5) = 5/7

⇒ 14x + 35 = 15x + 25

⇒ 15x – 14x = 35 – 25

⇒ x = 10

Number of students initially = 20, 30 and 50

Increased number of students = 25, 35, 55

Total number of increased students = 25 + 35 + 55 = 115

∴ The new total number of students in three hostels is 115.