- LPU MCA Semester 1
- PEA515
- Unit 4
PEA515 · Unit 4: Ratio, proportion and mixtures
Alligation rule
30 practice questions · in the ETE syllabus
Key points
- Cheaper : dearer = (dearer - mean) : (mean - cheaper)
- Subtract crosswise from the mean
- Convert selling price to cost price before alligation
- Pure ingredient quantity is unchanged when water is added
Alligation finds the ratio in which two ingredients of different prices (or strengths) are mixed to get a mixture of a given mean value. If the cheaper costs c, the dearer costs d and the mean is m, then
cheaper : dearer = (d - m) : (m - c).
Write the mean in the middle, the two prices on either side, and subtract crosswise: each ingredient's quantity is proportional to the distance of the other price from the mean. The same rule works for concentrations of solutions, for example mixing 25% and 35% solutions to get 29% needs them in the ratio (35 - 29) : (29 - 25) = 3 : 2.
| Problem | Idea |
|---|---|
| Ratio from prices | Alligation on cost prices |
| Mean price from a ratio | Weighted average |
| Selling price for a gain g% | Cost price x (100 + g) / 100 |
| Selling price given, ratio asked | Convert to the cost price first, then use alligation |
| Water added to a mixture | The quantity of the pure ingredient does not change |
Example: rice at 26 and 32 rupees per kg must give a mixture worth 27 rupees per kg, so cheaper : dearer = (32 - 27) : (27 - 26) = 5 : 1.
Exam trap: apply alligation to the cost price. If a selling price and a profit percentage are given, convert to cost first.
Try two questions
A 36 litre solution has 75% milk. Water is added until the milk is 50% of the total. How many litres of water are added?
- 9
- 18
- 54
- 19
Show the answer
B. Milk is 27 litres. For 50% milk the total must be 54 litres, so 18 litres of water are added.
Why not A: Takes the percentage drop of the original quantity.
Why not C: Gives the new total quantity instead of the water added.
Why not D: Arithmetic slip in the final step.
A chemist mixes a 19% salt solution with 32 litres of a 64% salt solution to obtain a 39% solution. How many litres of the 19% solution are used?
- 25.6
- 32
- 72
- 40
Show the answer
D. By alligation x : 32 = (64 - 39) : (39 - 19) = 5 : 4, so x = 40.
Why not A: Inverts the ratio of the two quantities.
Why not B: Assumes equal quantities of both solutions.
Why not C: Gives the total quantity of the mixture.