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General Intelligence & ReasoningMedium Level4 min readTopic 8 of 19

Arithmetical Reasoning

ssc-stenographer

Introduction

Arithmetical Reasoning combines basic maths (ages, ratios, simple arithmetic, time-distance) with logical setup. SSC Stenographer asks 2 to 3 such items per paper. They are scoring because the maths involved is class 7-8 level — the trick is forming the right equation from the word problem. After this lesson you will know the recurring question types and a step-by-step setup method.

Core Concept

Use the 4-step word-to-equation method:

1. Underline what is asked.
2. Assign one variable to the unknown closest to the answer.
3. Translate every sentence into an equation linking that variable.
4. Solve and verify by plugging back into the original story.

For age problems the formula (present age) ± n = (age n years ago/hence) handles every variant. For ratios, multiply each part by a common multiplier k. For coin problems, set up a value-per-coin × number-of-coins equation. Real-life analogy: think of the problem as a recipe — the variable is the missing ingredient, each sentence tells you a measurement.

Formula Sheet

TypeSetup
Age (present, past, future)Let A = present age; (A−n) = past, (A+n) = future
Sum of ages(A1+A2+...+An) given as one equation
Ratio splitParts in ratio a:b → ak and bk; total = (a+b)k
AverageAvg = Sum / Count
CoinsTotal value = Σ (denomination × count)

Solved Examples

Example 1. Father is 4 times as old as his son. After 5 years, he will be 3 times as old. Find their present ages.

  1. Let son's present age = x. Father = 4x.
  2. After 5 yrs: 4x + 5 = 3 (x + 5).
  3. 4x + 5 = 3x + 15 → x = 10.
  4. Son = 10, Father = 40.
  5. Verify: 45 = 3 × 15 ✓.
  6. Answer: Son 10, Father 40.

Example 2. Sum of three consecutive odd numbers is 75. Find the largest.

  1. Let smallest = x. Numbers: x, x+2, x+4.
  2. x + (x+2) + (x+4) = 75 → 3x = 69 → x = 23.
  3. Largest = 27.
  4. Answer: 27.

Shortcut: for "consecutive numbers sum" set the middle number = sum/count.

Question Patterns

  1. Age problems — present, past, future ratios.
  2. Ratio division — split a quantity in given ratio.
  3. Number of coins / notes — value-and-count equations.
  4. Average puzzles — adding/removing items affects average.
  5. Distance & time word problems — speed × time = distance.
  6. Logical sequence missing-number — hybrid of pattern and arithmetic.

Mistakes to Avoid

1. Setting the variable to the wrong unknown. Always assign the variable to what's directly asked.

2. Forgetting to add the time shift on both sides. "After 5 years" affects every age in the equation.

3. Mishandling ratios. Use a multiplier k; do not assume a:b means a units literally.

4. Skipping verification. A 5-second back-substitution catches arithmetic slips.

Exam Importance

ExamFrequencyMarksNotes
SSC StenographerHigh2–3Age and ratio dominate
SSC CGLHigh3–5Mixed types
RRB NTPCHigh3–4Average and ratio common

Why Arithmetical Reasoning is high-yield. SSC Stenographer 2026 asks 2–3 arithmetical-reasoning items every paper. Standard sub-types: ages (present-future-past relationships), ratio and proportion, percentage word problems, profit and loss, simple and compound interest, time-speed-distance, time-and-work, averages, mixtures and allegations. Build a one-page formula sheet. Ages: if A is currently x and B is y, then after t years their ages become x+t and y+t — set up the relation as an equation. Ratio: convert words to ratios first ("twice as old as" means 2:1; "5 years more" means add 5). Percentage: x% of y = xy/100; if a value increases by p% then decreases by p%, the net change = −p²/100. Profit/Loss: SP = CP × (1 + P%/100); discount on MP. SI = PRT/100; CI = P(1+r/100)ⁿ − P. TSD: speed = distance/time; relative speed for opposite direction = sum, same direction = difference. Time-Work: if A does work in x days, A's 1-day work = 1/x; combined work LCM method. Practise 10 arithmetical reasoning questions daily for 6 weeks. Cap each question at 50 seconds.

Quick Revision

  • Underline what is asked first.
  • Use one variable for the closest unknown.
  • Apply time-shift on both sides for age problems.
  • Use multiplier k for every ratio.
  • Coin problems: value × count.
  • Verify by back-substitution.
  • Aim 60 seconds per question.
  • Solve 10 PYQ word problems daily.
  • Age problems: 'A is twice as old as B' → A = 2B; 'X years ago' → (A−X) = relation × (B−X).
  • Ratio problems: A:B = 3:5 → A = 3k, B = 5k; sum/difference gives k directly.
  • Mixture problems: 'replace x litres of milk with water' → use ratio formula M(1−x/M)ⁿ.
  • Average problems: change in average × number = total change in sum.
  • Profit/loss in word form: SP = CP × (100 ± profit%)/100 — always check the percentage base.
  • Drill 100 SSC PYQ arithmetical-reasoning items to lock the recurring set-ups.

Test Yourself — 10 Questions

Score: 0 / 10

  1. Q1.A father is 4 times as old as his son. After 10 years, he will be twice as old. Find son's present age:

  2. Q2.Angle between hour and minute hand at 3:30:

  3. Q3.If today is Monday, what day will it be after 61 days?

  4. Q4.Average of 10, 20, 30, 40 is:

  5. Q5.20% of 250 is:

  6. Q6.Sum of two numbers is 50, their difference is 10. Larger number is:

  7. Q7.A clock shows 4:00. Angle between hands:

  8. Q8.If the day after tomorrow is Friday, what day was yesterday?

  9. Q9.A man scored 60 in Math, 70 in English, 80 in Science. Average:

  10. Q10.A is twice as old as B. Sum of their ages = 36. Find A's age:

Frequently Asked Questions

How many Arithmetical Reasoning questions appear in SSC Stenographer 2026?
Expect 2–4 Arithmetical Reasoning questions in SSC Stenographer 2026, worth 3–6 marks. Coverage includes age problems, calendar problems, clock problems, percentages, ratios, simple averages and word puzzles requiring basic arithmetic.
Which arithmetic topics are most asked in SSC Stenographer 2026 Reasoning?
Age problems (father-son, present-future), calendar (day of week calculations), clock angles, simple percentage calculations, profit/loss in word problems. SSC keeps the math basic — focus on speed not depth.
What is the formula for clock angle problems in SSC Stenographer 2026?
Angle between hour and minute hand = |(30H − 5.5M)| degrees, where H is hour and M is minutes. For 3:30, angle = |(30×3) − (5.5×30)| = |90 − 165| = 75°. Memorise this single formula — it solves all clock-angle questions.
How do I solve calendar problems in SSC Stenographer 2026?
Use the concept of odd days: 1 ordinary year = 1 odd day; 1 leap year = 2 odd days; 100 years = 5 odd days; 400 years = 0 odd days. Add odd days to a known date's day to find any future/past date's day.
What time should I cap on Arithmetical Reasoning in SSC Stenographer 2026?
Cap at 45 seconds per question. These mix logic with quick arithmetic — pre-memorised formulae (clock angle, age equations, percentage shortcuts) reduce solving time by 60%. Daily 10-question drill for 3 weeks builds the speed needed.
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