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Based on age, a class of students is divided into three groups, A, B and C, such that the sum of the ages of the students in the three groups is in the ratio 19 ∶ 21 ∶ 20. If a teacher of age 58 years is added to group A and another teacher of 22 years is added to group B, then a teacher of what age should be added to group C, so that the ratio of the sum of ages of the three groups become 1 ∶ 1 ∶ 1?

Based on age, a class of students is divided into three groups, A, B and C, such that the sum of the ages of the students in the three groups is in the ratio 19 ∶ 21 ∶ 20. If a teacher of age 58 years is added to group A and another teacher of 22 years is added to group B, then a teacher of what age should be added to group C, so that the ratio of the sum of ages of the three groups become 1 ∶ 1 ∶ 1? Correct Answer 40 years

Let the sum of the ages of students in groups A, B and C be ‘19x’ years, ‘21x’ years and ‘20x’ years respectively.

After adding teachers to groups A and B,

⇒ Sum of ages of group A = (19x + 58)

⇒ Sum of ages of group B = (21x + 22)

Final ratio of sum of ages of groups A and B = 1 ∶ 1

⇒ (19x + 58) = (21x + 22)

⇒ 2x = 36

⇒ x = 36/2 = 18

Now, let the age of teacher to be added in group C be ‘y’ years.

Sum of ages of group C = (20x + y) years

Also, final ratio of sum of ratio of groups B and C = 1 ∶ 1

⇒ (21x + 22) = (20x + y)

⇒ y = x + 22

Substituting for x,

⇒ y = 18 + 22 = 40 years

∴ A teacher of 40 years should be added to group C

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