Prelims · 8 Mental Ability · APPSC Group 2
8.4 Ratio, ages, averages and mixtures notes
10 notes, in reading order.
- 8.4.1Ratio and proportion
A ratio compares two quantities of the same kind by division; a proportion says two ratios are equal. Almost every ratio question is solved by writing each quantity as "parts" (3k, 4k) and finding the value of one part.
Standard · 9 min · Full course - 8.4.2Partnership: sharing profit by capital and time
Partners share profit (or loss) in the ratio of capital × time each one kept invested; a working partner's salary or commission is taken out first, and only the rest is shared by that ratio.
Standard · 8 min · Full course - 8.4.3Problems on ages
Age problems turn words into one or two linear equations; the key fact is that the difference between two people's ages never changes, while their ratio does.
Standard · 8 min · Full course - 8.4.4Averages: replacement, inclusion and exclusion
An average is total ÷ count, so nearly every average question is solved by converting averages into totals, adding or removing items, and dividing again.
Standard · 8 min · Full course - 8.4.5Mixtures and alligation
Alligation finds the ratio in which two ingredients must be mixed to get a given average (price, concentration, profit per cent); mixture questions are solved by tracking the one component whose quantity you know.
Standard · 8 min · Full course - 8.4.6Variation: direct, inverse and joint; mean and third proportional
"y varies as x" means y = kx for a fixed k; find k from the one case given, then use it for the case asked. Inverse, joint and square-root variation only change the formula, not the method.
Standard · 7 min · Full course - 8.4.7Chain rule: men, days, hours and work in proportion
When several quantities change together, link each one to the unknown as direct or inverse, multiply the ratios in a chain, or use the single formula M₁D₁H₁/W₁ = M₂D₂H₂/W₂.
Standard · 7 min · Full course - 8.4.8Repeated replacement in mixtures
Each time x litres are drawn from a full vessel of V litres and replaced with water, the original liquid is multiplied by (1 − x/V); after n times it is V(1 − x/V)ⁿ, like compound depreciation.
Standard · 7 min · Full course - 8.4.9Weighted averages and averages of consecutive numbers
A combined average weights each group by its size; and for numbers in equal steps the average is simply the middle term, which turns most "consecutive numbers" questions into one-line answers.
Standard · 7 min · Full course - 8.4.10Ratio word problems: coins, notes, salaries and distribution
Most ratio word problems hide one conversion: number of coins to their value, "4A = 5B" to a share ratio, or "A gets twice B" to parts; make that conversion first and the rest is one division.
Standard · 7 min · Full course
Practise Ratio, ages, averages and mixtures. Questions with answers explained, from the same topics.
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