Problems on Ages

Age problems look wordy but are pure ratio and linear-equation practice dressed in a story, and SBI Clerk usually rewards one or two of them each shift. The whole topic rests on one anchor: pick the present ages as your variables, then shift every person by the same number of years for the past or the future. Once you set the present up correctly, the arithmetic is a single equation. Speed here comes from a clean setup, not from clever tricks, so a disciplined starting line is everything.

Set Up From the Present

Let present ages be the unknowns, usually as a ratio like 4x and 5x when a ratio is given. For a time in the past, subtract the years from every age; for the future, add them to every age. The commonest slip is shifting only one person, so change all ages by the same amount every time. Writing 'x years ago' as (present − x) for each person, and 'after y years' as (present + y), keeps the equation honest and removes the most frequent source of wrong answers in this topic.

If present ages are in ratio a : b, take them as ax and bx, then apply the time shift to both

The Ratio-of-Ages Method

Many questions give a ratio now and a different ratio at another time, and ask for an actual age. Take the present ages as ax and bx, shift both by the stated years, set the shifted ages equal to the second ratio, and cross-multiply to find x. If ages are 4x and 5x now and become 5 : 6 after 4 years, then (4x + 4)/(5x + 4) = 5/6; cross-multiplying gives 24x + 24 = 25x + 20, so x = 4. This method cracks almost every two-ratio age problem in a couple of clean lines.

Sum and Difference of Ages

Two facts about age never change: the difference between two people's ages stays constant forever, while their sum increases by one year per person as time passes. If a father is 30 years older than his son today, he is 30 years older in any year, past or future. Use the fixed difference to shortcut questions that would otherwise need two variables — it often turns a two-equation problem into a single line and saves a genuine chunk of time on the clock.

Solved Examples

Example 1: Present ages are 5x and 7x, and after 6 years the ratio is 3 : 4. Then (5x + 6)/(7x + 6) = 3/4, so 20x + 24 = 21x + 18, giving x = 6; the ages are 30 and 42.

Example 2: A is twice as old as B and their ages sum to 45. Then 2B + B = 45, so B = 15 and A = 30 — no ratio shifting needed.

✗ Adding years to only one person when moving to the future  |  ✓ Shifting every person's age by the same number of years