- LPU MCA Semester 1
- PEA515
- Unit 4
PEA515 · Unit 4: Ratio, proportion and mixtures
Ratio and proportion
30 practice questions · in the ETE syllabus
Key points
- Share = ratio term x (amount / sum of terms)
- Extremes product equals means product
- Make the common term equal to combine ratios
- Inverse proportion keeps workers x days constant
A ratio compares two quantities of the same kind, written a : b, and does not change when both terms are multiplied or divided by the same number. A proportion states that two ratios are equal, a : b = c : d, and then product of extremes = product of means, so a x d = b x c.
| Task | Method |
|---|---|
Divide an amount in ratio a : b : c | One part = amount / (a + b + c); each share is its term x one part |
Fourth proportional in a : b = c : x | x = b x c / a |
Combine A : B and B : C | Make B equal in both, then read off A : B : C |
| Same number added to both terms | Write the numbers as ak and bk and solve for k |
| Direct proportion | Unit method: value of one, then multiply |
| Inverse proportion | workers x days stays constant |
Example: 63 rupees shared in the ratio 2 : 5 gives one part 63 / 7 = 9, so the shares are 18 and 45. For A : B = 9 : 2 and B : C = 7 : 9, A : B : C = 63 : 14 : 18, so A : C = 7 : 2.
Exam trap: an equal split ignores the ratio, and more workers means fewer days (inverse), not more.
Try two questions
The ratio of A to B is 9 : 2 and the ratio of B to C is 7 : 9. What is the ratio of A to C?
- 9 : 9
- 63 : 18
- 81 : 14
- 7 : 2
Show the answer
D. Make B equal in both ratios: A : B : C = 63 : 14 : 18, so A : C = 7 : 2.
Why not A: Takes the first and last terms without making the middle term equal.
Why not B: Multiplies the terms across without reducing.
Why not C: Cross multiplies the terms of the two ratios.
If 7 : 9 = 28 : x, find x.
- 36
- 21.78
- 30
- 63
Show the answer
A. In a proportion the product of extremes equals the product of means: 7 x x = 9 x 28, so x = 36.
Why not B: Cross multiplies the wrong pair of terms.
Why not C: Adds and subtracts the terms instead of using proportion.
Why not D: Multiplies the first two terms.