Ratios and their applications in Mixtures are a high-frequency topic in CAT Quant. This guided path will teach you the core skills, advanced problem-solving techniques, and the powerful shortcuts needed for a top score.
Start with the core definition of a ratio and walk through a step-by-step example of how to simplify ratios to their lowest terms.
A ratio compares values. Always express it in simplest form (like a fraction).
Car Zippy: $37,500
Car Giffy: $32,500
Ratio Z : G?
Divide by 100:
$$ 375 : 325 $$Both end in 5. Divide by 25:
$$ 375 \div 25 = 15 $$
$$ 325 \div 25 = 13 $$
Final Ratio: 15 : 13
Learn the fundamental method for solving word problems by representing unknown values with a common multiplier 'x'.
Multiply a ratio by a constant. The value remains the same.
Master the crucial technique for combining two separate ratios (e.g., a:b and b:c) into a single, continuous ratio (a:b:c).
Learn how to convert statements of multiples (e.g., 3A = 4B) into the correct A:B ratio, a common trap in advanced problems.
If 3A = 4B, what is A:B?
Rule: Inverse the coefficients.
$$ A:B = 4:3 $$If 2A = 3B = 4C, find A:B:C.
Step 1: Invert coefficients: $$ \frac{1}{2} : \frac{1}{3} : \frac{1}{4} $$
LCM of denominators (2, 3, 4) is 12.
Multiply each fraction by 12.
A: $$ \frac{1}{2} \times 12 = 6 $$
B: $$ \frac{1}{3} \times 12 = 4 $$
C: $$ \frac{1}{4} \times 12 = 3 $$
A:B:C = 6 : 4 : 3
Walk through a real-world application of ratios in partnership problems, where both investment and time must be considered.
When investment periods differ, profit is shared in the Compound Ratio of (Capital × Time).
A invests \$10k for 4 months.
B invests \$20k for 6 months.
C invests \$30k for 12 months.
Profit: \$7800.
Ratio: $$ 2:6:18 \rightarrow 1:3:9 $$
Total Parts: $$ 1+3+9 = 13 $$
1 Part = $$ 7800/13 = \$600 $$
A: \$600 | B: \$1800 | C: \$5400
Learn the powerful "Allegation" shortcut for solving mixture problems, and see how it's a visual representation of weighted averages.
A visual shortcut for mixture problems. Solves $$ \frac{w_1 C_1 + w_2 C_2}{w_1 + w_2} = \text{Mean} $$ without complex algebra.
Vessel A: 75% Spirit.
Vessel B: 40% Spirit.
Target Mixture: 60% Spirit.
Find Ratio A:B
$$ A : B = 20 : 15 $$
Ratio = 4 : 3
Put your understanding of CAT Ratio, Proportion & Mixtures: A Strategic Guide to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
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