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Ten percent of Max’s age was added to twenty percent of Dave’s age and the total was 24. Also, three times the age of Max exceeds the age of Dave by 20. What are the present ages of Max and Dave?

Ten percent of Max’s age was added to twenty percent of Dave’s age and the total was 24. Also, three times the age of Max exceeds the age of Dave by 20. What are the present ages of Max and Dave? Correct Answer 40, 100

Given∶

10% of Max’s age added to 20% of Dave’s age and the total was 24.

Also, 3 times the age of Max exceeds the age of Dave by 20.

Formula Used∶

Concept of Linear Equations, Elimination Method.

Calculation∶

Let the age of Max be ‘x’ years and Dave’s be ‘y’ years.

According to problem,

10% of x + 20% of y = 24

⇒ 10x/100 + 20y/100 = 24

⇒ x + 2y = 240     ----(1)

Also, 3x = y + 20

⇒ 3x – y = 20      ----(2) by

Multiplying eq. (2) by 2, we get

6x – 2y = 40 (3)

Add (1) and (2), we get

7x = 280

⇒ x = 40

Substituting x = 40 in eq.(1), we get

40x + 2y = 240

⇒ 2y = 200

⇒ y = 100

Hence, the present age of Max is 40 years and the age of Dave is 100 years.

(Dave was an American musician who died in 2019 at the age of 100 years.)

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