Ratio & proportion: Quantitative Aptitude Notes for Maharashtra PSC

Ratio & Proportion – Maharashtra PSC Quantitative Aptitude

Why it matters
Ratio & proportion questions are a staple of the Maharashtra PSC exam because they test a candidate’s ability to manipulate numerical relationships quickly and accurately. Mastery of this topic gives you a solid edge in sections like “Quantitative Aptitude (Easy)” and “Quantitative Aptitude (Medium)”.

1. Simple Explanation

Term	Definition	Example
Ratio	A comparison of two or more numbers by division.	If 8 apples cost ₹12, the ratio of apples to cost is 8 : 12 (can be simplified to 2 : 3).
Proportion	An equation that tells us two ratios are equal.	If the ratio of boys : girls in a class is 3 : 5, and there are 45 boys, the number of girls is 75 because 3/5 = 45/75.

Key idea – When you know two numbers in a ratio, you can find the third by setting up a proportion.

2. Key Points & Formulas

Concept	Formula	Notes
Basic Ratio	`a : b`	Use `a/b` to compare or convert to a proportion.
Proportion	`a : b = c : d` or `a/b = c/d`	Cross‑multiply to solve: `ad = bc`.
Finding a Number in a Ratio	If `x : y = m : n` and `x + y = S` → `x = (m/(m+n)) * S`, `y = (n/(m+n)) * S`.	Works for any two‑part ratio.
Compound Ratio	`(a : b) × (c : d) = (ac) : (bd)`	Useful for multi‑stage problems.
Percentage Ratio	`x : y = p : 100` → `x = (p/100) * (x+y)`	The part that is `p%` of the total.
Inverse Ratio	If `x : y = a : b`, then `y : x = b : a`.	Inverse ratio gives the reciprocal relationship.
Mean Proportion	Between `a` and `b` is `√(a*b)`.	Appears in problems involving geometric means.
Ratio in Terms of Sum	`x : y = m : n`, `x + y = S` → `x = (m/(m+n))S`, `y = (n/(m+n))S`.	Same as the “Finding a Number in a Ratio” formula.

3. Worked Example

Question
The ratio of the length to breadth of a rectangle is 3 : 4. If the perimeter is ₹28, find the area.

Step‑by‑Step Solution

Express the sides in terms of a common multiplier
Let the length = 3k and breadth = 4k.
Use the perimeter condition
[ 2(\text{Length} + \text{Breadth}) = 28 ] [ 2(3k + 4k) = 28 ;\Rightarrow; 14k = 28 ;\Rightarrow; k = 2 ]
Find actual dimensions
- Length = 3k = 6 units
- Breadth = 4k = 8 units
Compute the area
[ \text{Area} = \text{Length} \times \text{Breadth} = 6 \times 8 = 48 \text{ square units} ]

Answer: The area of the rectangle is 48 square units.

4. Quick Revision Summary

Ratio = a : b → compare two numbers.
Proportion = a : b = c : d → set up a*d = b*c.
Find a part when sum known → x = (m/(m+n))*S, y = (n/(m+n))*S.
Compound ratio → multiply numerators and denominators.
Percentage ratio → treat p% as part p out of 100.
Inverse ratio → swap the terms.
Mean proportion → √(a*b) for geometric mean.
Common Pitfall: Forget to simplify ratios before using them.
Speed Tip: Memorise the formula x = (m/(m+n))*S – it’s a one‑liner for most ratio‑sum problems.

Quick Practice Questions

In a group of 30 students, the ratio of boys to girls is 4:6. How many girls are there?
→ Girls = (6/(4+6))*30 = 18.
The ratio of two numbers is 5:7. If their sum is 72, find the larger number.
→ Larger = (7/(5+7))*72 = 42.
A shopkeeper sells a pair of shoes at ₹240, which is 20% of the cost price. Find the cost price.
→ Cost price = 240 / 0.20 = ₹1200.

Use these steps and formulas to tackle any ratio & proportion question in the Maharashtra PSC exam!