Arithmetic

Arithmetic – Verified PYQ Authority Guide

Arithmetic is a sub-subject authority hub. It is designed to expose the important topic/concept clusters represented by verified SRO PYQs and guide students from broad revision into the exact solved questions that support each area. 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

589 verified PYQs are currently mapped to this Sub Subject hub out of 614 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. 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…
3. 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 =…
4. 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…
5. 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…
6. 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.
7. 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…
8. If the principal is ₹1000, the rate is 5% per annum, and the time is 2 years, what is the simple interest?
   RRB NTPC Under Graduate Level · 2025 · Simple Interest Formula
   Simple interest is calculated only on the original principal. Using SI = (P × R × T) / 100 gives (1000 × 5 ×…

Formula & key-relationship bank from verified solutions

• Final Value = Initial Value × (1 − discount rate) × (1 + increase rate)
• 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
• Weighted Average = Σ(value × weight) / Σ(weights)

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.
• 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…
• Let the cost price of one pen be ₹1. Then 60 pens cost ₹60. The retailer sells those 60 pens for the purchase price of 72 pens, i.e. ₹72. Profit = ₹12, so profit% = 12/60 × 100…

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.
• 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.
• When article quantities are used in place of prices, assume unit cost ₹1 or form the SP:CP ratio directly.

Common mistakes to avoid

• Doing 25% − 20% = 5% and treating the final price as a simple 5% decrease from ₹4,000.
• 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.
• Dividing the profit by selling price 72 instead of cost price 60.

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, Time and Work. The concept trail includes Age Relations, Arithmetic Problem Solving, Ratio and Proportion, Profit and Loss, Discount, Simple Interest, Speed Time Distance, Combined Filling and Emptying. 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 Quantitative Aptitude, Ages, Arithmetic, Arithmetic Progression, Average, Average and Ratio, 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.