Arithmetical Reasoning
About 7 min · General Intelligence and Reasoning · English
Time worked out from the lesson's 472 words at 150 words a minute, plus a minute for each question.
Arithmetical Reasoning bridges logic and basic arithmetic. Unlike pure math problems, these questions wrap numerical operations inside a real-world story or logical scenario. You must first decode what the problem asks, then apply simple arithmetic (addition, subtraction, multiplication, division, or comparison) to reach the answer.
Key ideas
- Problem = Story + Arithmetic: Every question wraps a calculation inside a scenario. Identify the unknown, extract given numbers, and set up the operation.
- Keywords signal operations: "Total" or "altogether" suggests addition; "difference" or "how many more" suggests subtraction; "each" or "per" often means multiplication or division.
- Age problems: Relate present ages, past ages, or future ages using equations. Remember: if A is x years older than B now, A was also x years older y years ago.
- Distribution and sharing: When items are distributed equally, use division. When distribution is unequal, track each share separately and sum to check totals.
- Counting and arrangements: Problems may ask how many handshakes, matches, or steps occur. Use formulas (e.g., n people shaking hands once each = n(n−1)/2 handshakes) or systematic counting.
Watch out for
- Misreading the question: Students solve for the wrong variable. The problem asks for A's age, but you calculate B's age. Always underline or mentally note what is being asked before solving.
- Ignoring units or context: Computing 72 ÷ 8 = 9 is correct, but if the problem says "pencils cannot be broken," ensure 9 is a whole number. If not, re-check your setup.
- Confusing "more than" and "less than": "A is 5 more than B" means A = B + 5, not B = A + 5. Reverse logic leads to wrong equations and incorrect answers.
Quick reference
- Identify the unknown first: What is the question actually asking for? Circle or note it.
- Extract all given numbers and relationships: Write them down if the problem is complex.
- Set up the equation or operation: Translate words into math (sum → +, difference → −, each → ×/÷).
- Check consistency: Does your answer make logical sense? (e.g., no negative ages, no fractional people unless specified).
- Practice diverse types: Age, distribution, counting, averages, ratio-based word problems.
Check yourself: 3 questions
1. A vendor buys oranges at the rate of 5 for Rs 10. He wants to earn a profit of 20%. At what price per orange should he sell them?
2. A father is 3 times as old as his son. After 12 years, the father will be twice as old as his son. What is the present age of the son?
3. A cistern has two pipes. Pipe A can fill the cistern in 10 hours and Pipe B can empty it in 15 hours. If both pipes are opened simultaneously when the cistern is empty, in how many hours will the cistern be full?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.