Ratio and proportion sit at the heart of arithmetic reasoning. Almost every "shortcut" topic on a competitive exam — percentages, profit and loss, mixtures, time and work, speed, partnership, ages — is really a ratio problem in disguise. In BCS, bank (Combined/BB AD/Senior Officer) and IT-officer written and MCQ papers, you can expect 3–6 direct questions from this area, and dozens more that use it indirectly. Master this one topic well and a large slice of the quantitative section becomes fast and mechanical.
This lesson builds ratio, proportion and partnership from first principles, gives you the exact tools (unitary method, "k-method", componendo–dividendo, direct/inverse proportion), and drills them with full worked solutions.
Learning objectives
By the end of this lesson you will be able to:
- Define a ratio precisely and simplify, compare, combine, and split ratios.
- Divide a quantity in a given ratio (two-part and multi-part) with the k-method.
- Distinguish continued ratio, duplicate/triplicate ratios, and use them.
- State and apply the four terms of a proportion; use the property "product of extremes = product of means".
- Tell direct proportion from inverse proportion and set up each correctly.
- Apply mean proportional, third proportional, and fourth proportional.
- Solve simple, compound and time-based partnership problems (including working/sleeping partners and mid-year changes).
- Avoid the classic traps examiners plant in this topic.