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Playbook

Ratio, Proportion and Variation

76 q · 9% HARD · about 3.6 a paper. Ratio and proportion and variation have no HARD at all; partnership and mixtures carry the little there is.

Questions in the bank
76
q/paper (21 papers)
3.62
Tagged HARD
9%
Subtopics
6

Strand: Quick-Win

When you’ll see it

Quantities shared in a ratio, incomes and savings, variation, partnership or mixing two things.

How this chapter is tested

76 questions, about 3.6 a paper, at 9% HARD. Ratio and proportion and direct and inverse variation have never set a HARD question; partnership and mixtures carry what little there is.

Almost every question falls to one move: write each quantity as a multiple of one unknown k.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Sharing in a ratio

    A sum in the ratio a : b : c gives shares a/(a+b+c) of the total.

  • Ratios in stories

    Incomes, expenditures and savings, or ages before and after.

  • Equal ratios

    If a/b = c/d = k, write a = bk, c = dk.

  • Variation

    x varies as y: x = ky; inversely: xy = k.

  • Alligation

    Two mixtures at prices a and b make price m in the ratio (b − m) : (m − a).

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Ratio after a change

    Adding the same number to both terms changes the ratio.

  • Partnership by time

    Profit is shared in the ratio of capital × time, not capital alone.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.

Ratio, Proportion and Variation notes

Drill every Ratio, Proportion and Variation question

76 questions from the bank, across 6 subtopics.

Drill the 76 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

Related playbooks

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