# The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally, the total number of students is

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1. 100
2. 180
3. 200
4. 400

Option 3 : 200
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Telangana Police SI Preliminary Exam 2018 Official Paper 1
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200 Questions 200 Marks 180 Mins

## Detailed Solution

Given:

The students in three classes are in the ratio 2 ∶ 3 ∶ 5.

If 40 students are increased in each class, the ratio of the student in three classes becomes 4 ∶ 5 ∶ 7.

Calculation:

Let the number of students in three classes be 2x, 3x and 5x respectively.

When the numbers of students are increased by 40 in each class,

Then the number of students in three classes will be 2x + 40, 3x + 40 and 5x + 40 respectively.

According to the question,

(2x + 40) ∶ (3x + 40) ∶ (5x + 40) = 4 ∶ 5 ∶ 7

⇒ (2x + 40)/(3x + 40) = 4/5

⇒ (2x + 40) × 5 = (3x + 40) × 4

⇒ 12x – 10x = 200 - 160

⇒ 2x = 40

⇒ x = 20

The total number of students in the beginning = 2x + 3x + 5x = 10x

10x = 10 × 20 = 200

Originally, the total number of students is 200. Calculation:

The earlier ratio of students in three classes = 2 ∶ 3 ∶ 5

After increment, ratio of students = 4 ∶ 5 ∶ 7

The change in the ratio in each class = (4 – 2) = (5 – 3) = (7 – 5) = 2 unit.

2 unit given = 40

(2 + 3 + 5) unit = [40 × (2 + 3 + 5)]/2

⇒ 10 unit = (40 × 10)/2

⇒ 10 unit = 200

Originally, the total number of students is 200.
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