Rapid Revision · Quantitative Aptitude
Age problems are tiny linear equations dressed in stories. Fix 'now' as your reference point and translate each phrase carefully.
If you read nothing else tonight, read these 6 lines.
Every formula for problems on ages in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Shift in time
present = x -> t years ago = x - t, t years hence = x + t
Ratio now vs later
ages a:b now -> after t years: (ak + t) : (bk + t)
Introduce ONE variable k for the common ratio multiple, then solve.
Age difference is constant
(A - B) never changes with time
The single fact that cracks most age puzzles.
Sum & product
translate 'sum of ages', 'product', 'x times as old' into linear equations
6 cards, each one idea: what it is, a worked example, and the trap to dodge.
Assign variables to PRESENT ages. Each time phrase shifts every person by the same amount: '5 years ago' means subtract 5 from each.
Father is 3x son; 5 years ago he was 4x: 3s - 5 = 4(s - 5) gives s = 15, father 45.
Trap: Shifting only one person's age when the sentence shifts both.
Ratio p:q now means ages pk and qk. Apply the second condition to find k.
Ratio 4:5 now, 5:6 after 6 years: (4k+6)/(5k+6) = 5/6 gives k = 6, ages 24 and 30.
However far you go into the past or future, the gap between two people's ages is fixed. Many questions solve in one line with this fact.
Gap is 24 years and father is 3x son: 2s = 24, son 12, father 36.
Trap: Ratios are NOT constant over time; never carry a ratio across years unchanged.
The combined age of n people increases by exactly n x t in t years (ignoring births and deaths).
Family of 4 sums to 96 today; 5 years ago it was 96 - 20 = 76.
If the average age refuses to rise even though years passed, someone young joined. Write the total for both moments and balance.
5 people avg 30 today. In 5 years, with a new baby, avg is still 30: new total = 6 x 30 = 180; the old five will sum to 150 + 25 = 175, so the baby will be 5, meaning the baby is born now.
Trap: Write the totals for both moments explicitly; guessing the newcomer's age from the average alone usually goes wrong.
Two time conditions give two equations. Solve the pair; do not try to merge them into one ratio.
A was twice B's age 10 years ago and will be 1.5x in 10 years: a - 10 = 2(b - 10), a + 10 = 1.5(b + 10) gives b = 30, a = 50.
A recap is not practice. These are the creators we rate for real depth on problems on ages; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.