Quantitative Aptitude practice

Ratio and Proportion Questions with Answers

A ratio compares two quantities of the same kind, and a proportion says two ratios are equal. Ratio and proportion questions in SSC CGL, CHSL and MTS, RRB NTPC and Group D, and bank prelims ask you to share an amount, join ratios, find an unknown term, or work with mixtures. The same idea underlies partnership, ages and alligation. Tip: turn every ratio into 'parts' and find the value of one part first.

Formulas you need

Ratio a : b = a ÷ b; both terms must be in the same unit
If a : b = c : d, then ad = bc (cross-multiplication)
Dividing a total T in the ratio a : b : c gives parts T × a ÷ (a + b + c), and so on
To join a : b and b : c, make the common term b equal in both ratios
Compounded ratio of a : b and c : d = ac : bd
Duplicate ratio of a : b = a² : b²; triplicate = a³ : b³
Third proportional to a and b = b² ÷ a; mean proportional = √(ab)
Direct proportion: x ∝ y means x ÷ y is constant; inverse: x × y is constant
Mixture: add water to change ratio by keeping the quantity of milk constant

Worked examples

Q1. Divide ₹4,500 among three people in the ratio 2 : 3 : 4. Find each share.

Total parts = 2 + 3 + 4 = 9
One part = 4,500 ÷ 9 = ₹500
Shares: 2 × 500 = 1,000; 3 × 500 = 1,500; 4 × 500 = 2,000

Answer: ₹1,000, ₹1,500 and ₹2,000

Q2. A : B = 3 : 4 and B : C = 6 : 5. If ₹3,100 is divided among A, B and C in the ratio A : B : C, how much does C get?

Make B equal: A : B = 3 : 4 = 9 : 12 and B : C = 6 : 5 = 12 : 10
So A : B : C = 9 : 12 : 10
Total parts = 31, so one part = 3,100 ÷ 31 = ₹100
C = 10 × 100 = ₹1,000

Answer: ₹1,000

Q3. A 60-litre mixture contains milk and water in the ratio 7 : 3. How much water must be added to make the ratio of milk to water 7 : 5?

Milk = 60 × 7 ÷ 10 = 42 litres; water = 18 litres
Milk stays 42 litres. For ratio 7 : 5, water = 42 × 5 ÷ 7 = 30 litres
Water to add = 30 − 18 = 12 litres

Answer: 12 litres

Shortcuts that save time

Find the value of one part first. Once you know one part, every share is a simple multiplication, and you can check that the shares add up to the total before marking.
When joining two ratios, scale each ratio so the common term matches (use the LCM of the two values). Skipping this and multiplying straight across is the common source of wrong answers.
In mixture questions, track the quantity that does not change (milk in the example). Setting up with the unchanged part avoids the confusion that leads to wrong options.

Where this appears

SSC CGL Tier-1	Quantitative Aptitude section
SSC CHSL Tier-1	Quantitative Aptitude section
SSC MTS	Numerical and Mathematical Ability section
RRB NTPC CBT-1	Mathematics section
Bank PO/Clerk Prelims	Quantitative Aptitude section