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The ratio between the sum of the ages of 5 students of class A and that of 5 students of class B is 5 : 3. When a 15 years old student of class A is interchanged with a 10 years old student of class B, the ratio between the sum of ages of both the classes becomes 7 : 5. Find the ratio between the sum of the ages of remaining 4 students of class A to that of remaining 4 students of class B?

The ratio between the sum of the ages of 5 students of class A and that of 5 students of class B is 5 : 3. When a 15 years old student of class A is interchanged with a 10 years old student of class B, the ratio between the sum of ages of both the classes becomes 7 : 5. Find the ratio between the sum of the ages of remaining 4 students of class A to that of remaining 4 students of class B? Correct Answer 12 : 7

Let the sum of the ages of remaining 4 students of class A = a

And the sum of the ages of remaining 4 students of class B = b

Given,

(a + 15)/(b + 10) = 5/3

3a + 45 = 5b + 50

3a – 5b = 5      ---- (1)

Also given,

(a + 10)/(b + 15) = 7/5

5a + 50 = 7b + 105

5a – 7b = 55      ---- (2)

From equation (2) × 3 – equation (1) × 5

4b = 140

b = 35

From equation (1):

3a – 5 × 35 = 5

a = 60

Required ratio = 60: 35 = 12 : 7

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