Mixed Exam Age Patterns

🎯 Learning Objective

Tackle the toughest RRB age problems that combine 'years ago' and 'years hence' with ratios in one question.

💡 Concept

• Some questions fix the ratio at a PAST moment and ask about a FUTURE moment — anchor your variable at the past.
• If ages t years ago were ax and bx, then present = ax + t, bx + t, and h years hence = ax + t + h, bx + t + h.
• Keep a small time-line: past → present → future, and shift each expression carefully.
• Two conditions usually give one equation in x once the timeline is consistent.
• Always finish by translating x back into present ages or the asked ratio.

🧮 Key Formulas

Past ratio ax : bx → present ax + t, bx + t

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Future age = present + h

✏️ Easy Example

Q. A is twice as old as B. If A is 30 years old, find B's age.

1. A = 2 × B
2. 30 = 2 × B
3. B = 15

Answer: B = 15 years

🇮🇳 Real-Life Example

Family record books at a village panchayat often note ages at different events — a birth here, a marriage there — and reconciling them into today's ages is exactly this past-present-future juggling.

📝 Exam-Level Example

Q. 10 years ago, the ratio of the ages of A and B was 3 : 5. 10 years from now, the ratio will be 5 : 7. Find their present ages.

1. 10 years ago: A = 3x, B = 5x
2. 10 years hence (that is 20 years after the past point): A = 3x + 20, B = 5x + 20
3. (3x + 20)/(5x + 20) = 5/7
4. 7(3x + 20) = 5(5x + 20) → 21x + 140 = 25x + 100
5. 40 = 4x → x = 10
6. Present: A = 3x + 10 = 40, B = 5x + 10 = 60

Answer: A = 40 years, B = 60 years

📝 Exam-Level Example

Q. The age of a father 10 years ago was thrice the age of his son. 10 years hence, the father's age will be twice that of his son. Find the present ratio of their ages.

1. 10 years ago: son = s, father = 3s
2. Present: son = s + 10, father = 3s + 10
3. 10 years hence: son = s + 20, father = 3s + 20
4. 3s + 20 = 2(s + 20) → 3s + 20 = 2s + 40 → s = 20
5. Present: father = 70, son = 30 → ratio 70 : 30 = 7 : 3

Answer: Present ratio = 7 : 3

🪄 Memory Trick

Anchor your variable at the EARLIEST time mentioned. Every later age is then just that expression plus the elapsed years — no confusion.

⚠️ Common Mistakes

• ❌ Adding the wrong gap (past to future is t + h years, not just h)
• ❌ Anchoring at present but forgetting to subtract for the past condition
• ❌ Leaving the answer as x instead of the actual present ages

🏆 Exam Tips

• ✅ Sketch a tiny timeline with the two given moments before writing equations
• ✅ Double-check both conditions with your final ages, not just one

📌 Summary

• Anchor the variable at the earliest mentioned time
• Past→future gap = sum of both time shifts
• Same years added to every person
• Convert x back to present ages or the asked ratio