Problems Based on Ages

You are 20 and your uncle is 35. In 10 years you will be 30 and he 45 — but the gap of 15 years stays the same. That is the key to every age problem: the difference between two people’s ages never changes while their ratio changes every year. So most problems reduce to one linear equation; you only have to keep “today”, “ $n$ years ago” and “ $n$ years hence” straight.

(आज की आयु) \pm n = (n वर्ष बाद / पहले की आयु), अंतर = स्थिर

Two things that are always true

1

Age ratios

Years ago and years hence

Finding ages from the present ratio and the ratio $n$ years ago or hence.

The $k$ method

Write the ratio with

k

Take today’s ages as $x k$ and $y k$ and get $k$ from the condition.

Present ratio $x : y$ ⟹ ages $x k, y k$ .
“ $n$ years hence” ⟹ add $n$ to both; “ $n$ years ago” ⟹ subtract $n$ from both.
Equate the new ratio to the stated one, cross-multiply and find $k$ .
Check: is the difference between the two ages unchanged?

Example 1 · Basic

Two sisters’ ages are in the ratio 5 : 7. After 6 years the ratio becomes 7 : 9. Find their present ages.

Solution, step by step

1Ages $5 k, 7 k$ : $\frac{5 k + 6}{7 k + 6} = \frac{7}{9}$ ⟹ $45 k + 54 = 49 k + 42$ .
2 $4 k = 12$ ⟹ $k = 3$ ; ages 15 and 21 years.

Answer 15 years and 21 years

Example 2 · Standard

The sum of two friends’ ages is 60. After 5 years their ratio will be 3 : 4. What is the younger’s present age?

Solution, step by step

1After 5 years the sum is $60 + 2 \times 5 = 70$ ; split 3 : 4 gives $30$ and $40$ .
2Today both are 5 years less: $25$ and $35$ . The younger is $25$ .

Answer 25 years

Example 3 · Basic

Radha is 30 and Sita is 20. After 10 years what is the ratio of their ages and what is the gap?

Solution, step by step

1After 10 years the ages are $40$ and $30$ ⟹ ratio $4 : 3$ .
2The gap is $40 - 30 = 10$ — just as before.

Answer 4 : 3; gap 10 years

BasicTry it yourself first

Neeta’s and Gauri’s ages today are in the ratio 2 : 3. 6 years ago their ages were in the ratio 8 : 13. How old is Neeta today?

StandardTry it yourself first

Geeta’s and Meeta’s ages today are in the ratio 5 : 7. 6 years ago their ages were in the ratio 2 : 3. How old is Geeta today?

AdvancedTry it yourself first

Adi’s and Veer’s ages today are in the ratio 5 : 7. 9 years ago their ages were in the ratio 2 : 3. How old is Adi today?

BasicTry it yourself first

Two people’s ages today are in the ratio 5 : 7. After 4 years the ratio becomes 3 : 4. How old is the elder one today?

StandardTry it yourself first

Two people’s ages today are in the ratio 5 : 7. After 5 years the ratio becomes 3 : 4. How old is the younger one today?

AdvancedTry it yourself first

Two people’s ages today are in the ratio 4 : 5. After 12 years the ratio becomes 5 : 6. How old is the elder one today?

StandardTry it yourself first

The sum of two friends' present ages is 60 years. After 5 years their ages will be in the ratio 33 : 37. What is the present age of the elder?

AdvancedTry it yourself first

The sum of two friends' present ages is 96 years. After 8 years their ages will be in the ratio 13 : 15. What is the present age of the elder?

2

Multiple-type questions

From “

m

times” to “

n

times”

Today one is $m$ times the other; $t$ years hence / ago $n$ times.

One unknown, one equation

Take the younger’s age as

x

Call the younger $x$ and the elder $m x$ ; shift the time and form the equation.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

3

Average age and timelines

Total age and counting events

Family or class average ages, a three-person ratio, the middle person and event timelines.

Averages, ratios and timelines

Total = average × number

Solve average-age questions through the total age; in timelines add the durations.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

4

Traps and fast tricks

Slips · tricks

Where marks go in age questions.

The commonest mistakes

Six traps

The slips that cost marks.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

Fast tricks

The gap and the options

Habits for speed.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

5

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

Level 2 — Standard

Two ideas combined

Exam-level questions.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

6

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

🔒

This part is in All Access.

With the pass, every example, practice question and solution in this chapter opens.

See the pass · ₹100.00 Already have a pass? Sign in

Also in these passes: RAS Pre 2026 — 40 Day Study Plan + Complete Notes (₹300.00) · Competitive Maths (English Medium) (₹90.00) · RRB NTPC Graduation Level 2026 (₹300.00) · RRB NTPC Under Graduate Level 2026 (₹300.00)

Age ratios

The $k$ method

Multiple-type questions

One unknown, one equation

Average age and timelines

Averages, ratios and timelines

Traps and fast tricks

The commonest mistakes

Fast tricks

The practice ladder

Level 1 — Basic

Level 2 — Standard

Level 3 — Advanced

Revision — formula cards

Free All Access Passevery mind map · Hindi + English · 12 months

How is it going?