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Ratios and ages

Share ₹1,200 in the ratio 3 : 5, chain A : B with B : C, find an age from what it will be — one part first, then count the parts.

  • Quantitative reasoning
  • Untimed
  • Endless levels

How it plays

Each question is a ratio or a proportion: scale one, divide a sum by one, chain two through the term they share, or decide whether doubling one thing doubles or halves another.

New kinds unlock as you climb — ages now and later, partners paid by money × months, a ratio that changes when something is added — and the numbers grow without end. Ages stay human.

The wrong options are the real slips: the ratio read backwards, two ratios joined without matching the shared term, a direct proportion where it is inverse, the age in the future given for the age now.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This makes ratio, proportion and age problems of these kinds quicker and surer. It claims nothing wider.

Learn

How to get better at ratios and ages: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Find the value of one part first. Whatever the question, a ratio is a count of equal parts; once you know what one part is worth, everything else is counting.
  2. Read the order of the ratio as written. “Boys to girls is 3 : 5” puts boys first; keep every later number in that order.
  3. For two quantities that move together, ask whether doubling one doubles the other (direct: more notebooks, more cost) or halves it (inverse: more speed, fewer hours).
  4. For ages, write the ages now as unknowns, move both forward or back by the same years, and use the condition. Check that the answer is a sensible human age and fits every sentence.

Techniques and tricks

  • Total ÷ parts, then times parts

    To share a sum in a ratio, add the parts, divide the total by that to get one part, then multiply by each person’s parts.

    e.g. ₹1,200 in 3 : 5: 8 parts, one part ₹150, so ₹450 and ₹750

  • Given one side, find the part

    When you are told one side of a ratio, divide it by its own number of parts. That is one part; multiply by the other side’s parts.

    e.g. boys : girls = 3 : 5 with 24 boys: one part is 8, so 40 girls

  • Chain ratios through the shared term

    To join A : B with B : C, scale both so B is the same number in each. Multiplying the first by the second’s B and the second by the first’s B always works; then reduce.

    e.g. A : B = 2 : 3, B : C = 4 : 5 → 8 : 12 and 12 : 15 → 8 : 12 : 15

  • Direct or inverse: what stays fixed?

    If the price per item is fixed, cost goes with the count. If the distance is fixed, time goes against the speed: multiply speed by time to get the fixed amount, then divide by the new speed.

    e.g. 4 hours at 60 km/h is 240 km; at 80 km/h, 240 ÷ 80 = 3 hours

  • The age gap never changes

    Two people’s ages differ by the same number of years forever. If A is m times B now, the gap is (m − 1) × B’s age; set that equal to the gap the later condition gives.

    e.g. A is 3 times B; in 10 years A is twice B. Then the gap 2b equals B’s age then, b + 10, so b = 10 and A is 30

  • Totals move by twice the years

    For two people, the sum of their ages t years ago was the sum now minus 2t. Split that past total in the given ratio, then add t back to each.

    e.g. total 50 now; 5 years ago A was 3 times B: then 40 split 3 : 1 is 30 and 10, so now 35 and 15

  • Partners: money × months

    Profit is shared in the ratio of each partner’s money times the months it was in. Work in thousands to keep the numbers small, then reduce the ratio and share as usual.

    e.g. ₹20,000 for 9 months against ₹30,000 for 4: 180 : 120 = 3 : 2, so ₹10,000 profit gives ₹6,000 and ₹4,000

As the levels climb

  • The kinds unlock in this order: scaling a ratio, dividing in a ratio, and direct or inverse proportion; then chaining two ratios and “times as old”; then ages from a ratio now and later, and from a sum and the past; then partners and profit, and a ratio that changes when something is added. Four in ten questions come from the newest kind.
  • The numbers grow as you climb — bigger ratios, larger sums, three-way shares — but the ages stay human and every answer comes out whole. A fraction in your working means a slip.
  • At the last tier, look for what does not change. When red counters are added, the blue stay put: write the blue in both ratios and the red follows.
  • Each step of size adds 8% to the time, up to twelve steps. Typed answers must be exact; chained ratios are typed in lowest terms, like 8:12:15.

Traps to avoid

  • The ratio read backwards: with 3 : 5 and the 3 side given, finding the 5 side by dividing the wrong way. Say which side is which, out loud, before you divide.
  • Two ratios joined without matching the shared term: 2 : 3 and 4 : 5 written straight together as 2 : 3 : 5. B is 3 in one and 4 in the other, so neither ratio can be used until they agree.
  • Direct where it is inverse: going faster and answering more hours. If one thing goes up and the other must come down, multiply to the fixed amount and divide.
  • The age in the future given for the age now: the equation gives b, which is the age now — not b + 10. Read which moment the question asks about.
  • Profit split by money alone, or by months alone: a partner who put in more for less time can earn the same. Multiply the two together first.

How to practise

  • In “Kinds of question”, drill the three age kinds together until setting up the ages now, then moving them, is routine.
  • Switch “Answer by” to “Typing the answer”. Answers must be exact, which makes you finish the working rather than recognise a nearby option.
  • Raise “Options shown” towards 8 to see the backwards ratio, the unmatched chain and the future age at once.
  • Read the working after each miss: it always finds one part first, and that step is usually the one a miss skipped.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More quantitative reasoning

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