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PROBLEMS ON AGES

PROBLEMS ON AGES – FULL CONCEPT REVISION

1. Important Formulas

Concept	Formula/Relation
Present Age	Assume as variable (x, y etc.)
Past Age	= Present Age – years
Future Age	= Present Age + years
Ratio of Ages	Use direct proportion
Average Age	= (Sum of ages) ÷ (Number of persons)
Age difference	Always constant over time
Linear Equation Trick	If “after n years” or “before n years” is common → use variable substitution to form equation

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2. Quick Tricks

1. “Before or After” → use same ‘n’ in all ages
2. Difference always remains same — helps to check answers fast.
3. Ratio conversion:
   • If ratio = 3 : 5 → assume ages = 3x, 5x
4. Average method:
   • If average increases by n years → total age increased by (n × number of persons).
5. When question says ‘twice/half/three times older’ → make equation directly.
6. Smart tip: Always check if difference of your answer matches question condition.

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EASY LEVEL (10 Questions)

1️⃣

Father’s age is twice that of his son. If father is 36, what is son’s age?
2️⃣

Sum of ages of A and B is 50. A is 4 years older than B. Find A, B.

3️⃣

Age of Ram is 4 years more than twice Shyam’s. If Ram is 18, find Shyam’s age

4️⃣

5 years ago, A was 10 years old. Find his present age.
5️⃣

After 6 years, Ravi will be 25. Find his present age.

 

6️⃣

If father’s age is 30 and son’s age is 10, after how many years father will be twice as old as son?

 

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7️⃣

Age of a man 5 years ago was 8 years less than twice his son’s age. If son’s present age is 10, find man’s present age.

 

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8️⃣

Average age of 4 persons is 25. Find total of their ages.

 

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9️⃣

If the ratio of ages of two friends is 3:4 and sum is 56, find their ages.

 

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🔟

Ramesh is 5 years younger than Suresh. If Ramesh is 25, find Suresh’s age.

MEDIUM LEVEL (10 Questions)

1️⃣

Ten years ago, father’s age was thrice the son’s age. After 10 years, it will be twice. Find present ages.

 

2️⃣

Sum of ages of A, B, C is 90. After 5 years, their ages will be in ratio 2:3:4. Find present ages.

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3️⃣

A’s age is twice B’s and thrice C’s. If sum = 110, find their ages.

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4️⃣

The average age of a father and two sons is 27. If father’s age is 45, find average of sons.

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5️⃣

After 4 years, the ratio of A and B will be 5:7. Four years ago, it was 1:2. Find their present ages

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6️⃣

Present ages are in ratio 7:3. After 6 years, the ratio becomes 2:1. Find present ages.

 

7️⃣

A is 3 years older than B. 5 years ago, ratio was 4:5. Find present ages.

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8️⃣

The sum of ages of father and son is 60. 5 years ago, father’s age was 4 times son’s. Find present ages.

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9️⃣

4 years ago, mother was 3 times the daughter’s age. After 8 years, she will be twice. Find present ages.

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🔟

Age of a father is 4 times son’s. After 20 years, sum of their ages is 100. Find their present ages.

ADVANCED LEVEL (10 Questions)

1️⃣

The ratio of ages of A and B is 4:3. After 6 years, the ratio becomes 9:7. Find their present ages.
2️⃣

Father is 5 times the age of his son. 5 years ago, he was 7 times. Find present ages.

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3️⃣

The age of the father is twice the sum of the ages of his two children. After 20 years, sum of their ages will be 150. Find father’s present age.

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4️⃣

Sum of ages of A, B, C, D is 80. 5 years ago, ratio was 1:2:3:4. Find A’s present age.

 

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5️⃣

A’s age after 15 years will be 5 times his age 10 years ago. Find present age.

 

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6️⃣

Average age of 3 friends is 20. A leaves and new average becomes 19. A’s age was?

 

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7️⃣

Sum of ages of A and B is 56. Ratio after 4 years becomes 5:3. Find present ages.
8️⃣

A’s age is 150% of B’s and 50% of C’s. Find ratio A:B:C

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9️⃣

Age of a teacher is 4 times average age of his 5 students. If average of all 6 is 19, find teacher’s age

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🔟

4 years ago, the average of A, B, and C was 20. Today the ratio is 3:4:5. Find their present ages.
Summary Tips for Students

1. Always form equations smartly; don’t panic with wording.
2. Remember difference constant rule – powerful shortcut.
3. In exams, check ratio matching for fast elimination.
4. Use average → total → back-calculate trick.
5. Practice mental calculation for +/– years adjustments.