Ratio & Proportion — RRB NTPC Mathematics
This topic carries roughly 7% of Mathematics's 30 questions, and its logic reappears inside Time & Work and Time & Distance problems elsewhere in the paper — a ratio, at its core, is just a comparison, and proportion is what happens when two ratios are set equal.
1. What RRB NTPC actually asks
Expect direct ratio division of a total quantity, combining two ratios that share a common term (a:b and b:c to find a:b:c), mean proportional problems, and direct-versus-inverse proportion word problems.
2. Dividing a quantity in a given ratio
To split a total T in the ratio a:b:c, divide T into (a+b+c) equal parts, then assign a parts, b parts, and c parts respectively. Each share = T × (its ratio term) / (sum of all ratio terms).
3. Combining two ratios
Given a:b and b:c, to find a:b:c, scale both ratios so the common term (b) matches in both — use the LCM of the two b-values as the shared middle term, then scale a and c to match.
4. Mean proportional
The mean proportional between two numbers p and q is √(pq) — the number m such that p:m = m:q.
5. Direct vs inverse proportion
Direct proportion: as one quantity increases, the other increases at the same rate (more pens cost more money — cost/pens stays constant).
Inverse proportion: as one quantity increases, the other decreases proportionally (more workers finish a job faster — workers × days stays constant).
Mixing these up is the single most common error in this topic — always ask whether the two quantities should move in the same direction or opposite directions before setting up the equation.
Worked examples
Q1. Divide ₹720 among A, B, and C in the ratio 2:3:4. What is C's share?
Pick an option to check your answer.
Show explanation
Solution. Total parts = 2+3+4 = 9. Each part = 720/9 = 80. C's share = 4 parts = 4 × 80 = 320.
A gets 2 × 80 = 160 and B gets 3 × 80 = 240 — these are the other two options, not C's share. Answer: (c).
Q2. 35 workers can complete a task in 12 days. How many days will 21 workers take to complete the same task, working at the same rate?
Pick an option to check your answer.
Show explanation
Solution. This is inverse proportion: fewer workers take more days, and workers × days stays constant. 35 × 12 = 21 × d, so d = 420/21 = 20.
A common error is treating this as direct proportion (fewer workers, fewer days), which would give an answer smaller than 12 instead of larger — always sanity-check the direction before computing. Answer: (c).
7. Common traps
- Confusing direct and inverse proportion. Ask first whether the two quantities should move in the same or opposite directions.
- Using the wrong common term when combining two ratios. Always scale so the shared middle term (b, in a:b and b:c) matches exactly in both before combining.
- Forgetting to divide by the sum of ratio terms, not by the number of terms — dividing 720 by 3 (the count of terms) instead of 9 (their sum) is a common slip.
- Computing mean proportional as the simple average instead of √(pq). The mean proportional and the arithmetic mean are different quantities.
8. Guessing strategy
For direct/inverse proportion word problems, a quick direction check (should the answer be larger or smaller than the given comparable value?) eliminates roughly half the options immediately, clearing the guessing threshold under 1/3 negative marking.
Summary
- Ratio & Proportion is roughly 7% of Mathematics's 30 CBT 1 questions.
- To split a total in ratio a:b:c, divide by the sum (a+b+c), not the count of terms.
- To combine a:b and b:c into a:b:c, scale both ratios so the shared term matches using their LCM.
- Mean proportional between p and q is √(pq), not their arithmetic average.
- Direct proportion: quantities move together. Inverse proportion: quantities move oppositely — mixing these up is the most common error.
- A quick "should this answer be bigger or smaller" direction check usually clears the guessing threshold.
