Quantitative Aptitude

Quantitative Aptitude – Verified PYQ Authority Guide

Quantitative Aptitude is a subject-level PYQ authority hub. The page summarises where the verified corpus is concentrated, which topics/concepts recur, and where students can continue into detailed question-level solutions. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.

PYQ evidence snapshot

765 verified PYQs are currently mapped to this Subject hub out of 790 total mapped questions. The represented years include 2025. Exam coverage currently includes RRB NTPC Under Graduate Level. Subject context includes Quantitative Aptitude. These values come from live mappings and can expand automatically when new verified PYQs are added.

Most useful verified PYQs to solve first

Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.

1. A shopkeeper marks an item at ₹4,000. During a festival, he first offers a discount of 25% on the marked price. After a week, he increases the discounted price by 20% to…
   RRB NTPC Under Graduate Level · 2025 · Discount Followed by Price Increase
   After a 25% discount, ₹4,000 becomes ₹3,000. Increasing ₹3,000 by 20% adds ₹600, giving a final selling price of ₹3,600.
2. If sin 6A = cos 12A, find the value of tan 9A + cot 9A.
   RRB NTPC Under Graduate Level · 2025 · Using sin θ = cos(90° − θ)
   Using cos 12A = sin(90° − 12A), the standard relation gives 6A + 12A = 90°, so A = 5°. Then 9A = 45°,…
3. A train runs at 72 km/h for 3 hours and then at 60 km/h for 1.5 hours. What is the average speed of the train?
   RRB NTPC Under Graduate Level · 2025 · Average Speed for Unequal Time Intervals
   Total distance = 72×3 + 60×1.5 = 216 + 90 = 306 km. Total time = 4.5 h. Average speed = 306/4.5 = 68…
4. The ages of two siblings add up to 44 years. If one sibling is 4 years younger than twice the other's age, what is the difference between their ages?
   RRB NTPC Under Graduate Level · 2025 · Age Sum and Relationship Equations
   Let the younger-reference sibling be x years. The other is 2x − 4. Then x + (2x − 4) = 44, so 3x =…
5. A shopkeeper offers the following schemes on toys of the same marked price. (A) Successive discounts of 44% and 12% on any number of toys bought. (B) Successive discounts of 18%, 43%…
   RRB NTPC Under Graduate Level · 2025 · Comparison of Discount Schemes
   Assume each toy is marked ₹100. For 10 toys, payable amounts are: A ₹492.80, B ₹359.898, C ₹740 and D ₹700. The customer pays…
6. A retailer buys 60 pens and sells them at the purchase price of 72 pens. Determine his profit percentage.
   RRB NTPC Under Graduate Level · 2025 · Profit Percentage from Quantity Equivalence
   Let the cost price of one pen be ₹1. Then 60 pens cost ₹60. The retailer sells those 60 pens for the purchase price…
7. A student scores 75, 80 and 90 in three tests with weights 2, 3 and 5 respectively. What is the weighted average score?
   RRB NTPC Under Graduate Level · 2025 · Weighted Mean Formula
   Multiply each score by its weight and divide by the total weight: (75×2 + 80×3 + 90×5) / (2+3+5) = 840/10 = 84.
8. If 5 and 10 are given, what is the third proportional to these numbers?
   RRB NTPC Under Graduate Level · 2025 · Third Proportional
   If c is the third proportional to a and b, then a : b = b : c. Thus 5 : 10 = 10…

Formula & key-relationship bank from verified solutions

• Final Value = Initial Value × (1 − discount rate) × (1 + increase rate)
• cos θ = sin(90° − θ); tan 45° = 1; cot 45° = 1
• Average Speed = Total Distance / Total Time
• If ages are x and 2x − 4, then x + 2x − 4 = 44
• Successive price factor = (1 − d1)(1 − d2)...; Effective discount = 1 − final price factor
• Profit % = (SP − CP) / CP × 100

Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.

Core ideas repeatedly reinforced by the solved corpus

• After a 25% discount, ₹4,000 becomes ₹3,000. Increasing ₹3,000 by 20% adds ₹600, giving a final selling price of ₹3,600.
• Using cos 12A = sin(90° − 12A), the standard relation gives 6A + 12A = 90°, so A = 5°. Then 9A = 45°, and tan45° + cot45° = 1 + 1 = 2.
• Total distance = 72×3 + 60×1.5 = 216 + 90 = 306 km. Total time = 4.5 h. Average speed = 306/4.5 = 68 km/h.
• Let the younger-reference sibling be x years. The other is 2x − 4. Then x + (2x − 4) = 44, so 3x = 48 and x = 16. The other age is 28, giving a difference of…
• Assume each toy is marked ₹100. For 10 toys, payable amounts are: A ₹492.80, B ₹359.898, C ₹740 and D ₹700. The customer pays the most under Scheme C, so Scheme C is least beneficial. Scheme C is…

Exam tips already validated in SRO solutions

• Convert each percentage change to a multiplier and apply them in order; it is usually faster than calculating rupee changes separately.
• For sin x = cos y questions, first test the complementary relation x + y = 90°; it often leads directly to a standard angle.
• Use total distance ÷ total time unless a special equal-distance shortcut is clearly applicable.
• Translate phrases exactly: '4 younger than twice x' means 2x − 4, then verify the solved ages in both conditions.
• For mixed discount schemes, assume marked price ₹100 per item and compare the final payable amount rather than trying to compare percentages mentally.

Common mistakes to avoid

• Doing 25% − 20% = 5% and treating the final price as a simple 5% decrease from ₹4,000.
• Stopping after tan45° = 1 and forgetting to add cot45° = 1.
• Taking (72 + 60)/2 = 66 km/h even though the train spends different amounts of time at the two speeds.
• Writing 2(x − 4) instead of 2x − 4.
• Adding successive discount percentages directly or forgetting that Scheme C applies different discounts to different quantities.

Topic and concept coverage

Mapped topic labels include Profit, Loss and Discount, Ratio and Proportion, Problems on Ages, Quantitative Aptitude, Speed, Time and Distance, Interest, Number Properties. The concept trail includes Age Relations, Arithmetic Problem Solving, Ratio and Proportion, Profit and Loss, Algebraic Simplification, Discount, Trigonometric Ratios, Simple Interest. Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.

Knowledge Graph navigation

Continue with Algebra, Arithmetic, Geometry, Number System, Speed Time and Distance, Profit, Loss and Discount, General Arithmetic, Quantitative Aptitude, Ratio and Proportion, Proportion. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.

How to revise this authority page efficiently

1. Solve before reading: answer a mapped PYQ first.
2. Read the exact explanation: verify the correct principle, formula, distractor logic and common mistake on that question page.
3. Move one level in the graph: use the closest concept/sub-topic/topic link rather than opening unrelated content.
4. Reattempt: solve another verified PYQ from this hub and check whether the same error repeats.

Quality scope: this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.