Jacob was 60 months old when Patrick joined the company. Patrick had joined…
2025
Jacob was 60 months old when Patrick joined the company. Patrick had joined company 80 months back. Martin is now eighty months more than six times the age of Jacob when Patrick joined company. The total of the ages of Jacob, Patrick and Martin is 100 years after lapse of 8 1/3 years. What was the age at which Patrick joined company ?
- A.
20 years
- B.
28 years
- C.
24 years
- D.
30 years
Attempted by 6 students.
Show answer & explanation
Correct answer: A
Answer: 20 years
Let P be Patrick's age when he joined, measured in months.
Jacob's age when Patrick joined = 60 months. Patrick joined 80 months ago, so Jacob's current age = 60 + 80 = 140 months.
Patrick's current age = P + 80 months.
Martin's current age = 6 × (Jacob's age when Patrick joined) + 80 = 6 × 60 + 80 = 440 months.
After 8 1/3 years = 25/3 years = 100 months, each person ages by 100 months, so the total increases by 3 × 100 = 300 months. The total after that lapse is 100 years = 1200 months.
Therefore current total (in months) = 1200 − 300 = 900 months.
Set up the equation for current ages: 140 + (P + 80) + 440 = 900.
Simplify: P + 660 = 900 ⇒ P = 240 months = 240/12 = 20 years.