Arithmetic Reasoning

Arithmetic Reasoning is the application of basic arithmetic operations to solve real-life logical and mathematical problems. It includes:

Number puzzles
Age problems
Time-speed-distance
Profit-loss
Ratio-proportion
Simple equations
Mixed word problems

These problems test both logical and mathematical thinking.

🧮 2. Key Topics in Arithmetic Reasoning

S.No	Topic	Examples Include
1	Number Series	Find the missing number
2	Age Problems	Age now, past/future age
3	Time-Speed-Distance	Train, boat, walking problems
4	Profit & Loss	CP, SP, profit%, loss%
5	Ratio & Proportion	Mixture problems, shares
6	Simple & Compound Interest	Interest over time
7	Work & Wages	Men-day problems
8	Boats and Streams	Upstream/downstream speed

🔧 Important Methods & Shortcuts

✅ Basic Arithmetic Operations

Addition, Subtraction, Multiplication, Division
BODMAS Rule (Bracket, Order, Division, Multiply, Add, Subtract)

✅ Key Formulas to Remember:

Concept	Formula
Profit%	`(Profit / CP) × 100`
Loss%	`(Loss / CP) × 100`
Speed	`Distance / Time`
Average	`Sum of observations / Number of items`
Work Efficiency	`Work = Rate × Time`
Compound Interest (CI)	`CI = P(1 + r/100)^t – P`

🧩 Examples with Diagrams & Explanations

🔹 Example 1: Age Problem

Q: A father is 4 times the age of his son. In 10 years, he will be 2 times the age of his son. Find the current age of father and son.

✅ Let son’s age = x
→ Father = 4x
After 10 years:
Father = 4x + 10
Son = x + 10
Now:
4x + 10 = 2(x + 10)

➡️ Solve:

4x + 10 = 2x + 20  
2x = 10  
x = 5 (Son)  
Father = 20

✅ Answer: Son = 5, Father = 20

🔹 Example 2: Profit and Loss

Q: A man buys a watch for ₹1200 and sells it at a 20% profit. What is the selling price?

✅ SP = CP × (1 + Profit%)
= 1200 × (1 + 20/100) = 1200 × 1.2 = ₹1440

✅ Answer: ₹1440

🔹 Example 3: Time-Speed-Distance

Q: A train runs at 60 km/h. How much time will it take to cover 180 km?

✅ Time = Distance / Speed = 180 / 60 = 3 hours

✅ Answer: 3 hours

Diagram:

Train ➡️ ——180 km—— 🕒 = 3 hr at 60 km/h

🔹 Example 4: Number Series

Q: What comes next in the series: 2, 4, 8, 16, __?

Pattern: ×2
Next = 16 × 2 = 32

✅ Answer: 32

🔹 Example 5: Work and Wages

Q: A can complete a work in 10 days. B can do it in 15 days. How long will they take together?

✅ Formula:
Work/day = A + B = (1/10 + 1/15) = (3 + 2)/30 = 5/30 = 1/6
Time = 6 days

✅ Answer: 6 days

📊 Visual Diagram Summary

👉 Common Problem Format:

[Real-world statement] ➝ Convert to math ➝ Apply formula ➝ Solve

🧠 BODMAS Rule Reminder:

Brackets → Orders → Division → Multiplication → Addition → Subtraction

📚 Quick Practice Challenge

Q: The average of 5 numbers is 42. The average of the first four numbers is 40. What is the 5th number?

✅ Total of 5 = 5 × 42 = 210
Total of 4 = 4 × 40 = 160
So 5th number = 210 – 160 = 50

✅ Answer: 50

📝 Tips for Exam Success

Always read the question twice.
Convert word problems to equations.
Use elimination method in MCQs.
Estimate to save time when exact values aren’t needed.

✅ Practice Questions - Arithmetic Reasoning

🔹 Q1. Age Problem

Q: A is 3 years older than B. 5 years ago, A was twice as old as B. What is their present age?

Solution:
Let B = x → A = x + 3
5 years ago:
(x + 3) – 5 = 2(x – 5)
x – 2 = 2x – 10 → x = 8 → A = 11

✅ Answer: A = 11 years, B = 8 years

🔹 Q2. Profit & Loss

Q: A shopkeeper sells an item for ₹240 at 20% profit. What is the cost price?

Solution:
SP = CP × (1 + 20/100) = CP × 1.2
So CP = 240 / 1.2 = ₹200

✅ Answer: ₹200

🔹 Q3. Time-Speed-Distance

Q: A train travels 300 km in 5 hours. What is its speed?

Solution:
Speed = Distance / Time = 300 / 5 = 60 km/h

✅ Answer: 60 km/h

🔹 Q4. Simple Interest

Q: What is the simple interest on ₹5000 for 2 years at 10% per annum?

Solution:
SI = (P × R × T) / 100 = (5000 × 10 × 2) / 100 = ₹1000

✅ Answer: ₹1000

🔹 Q5. Number Series

Q: What comes next: 5, 10, 20, 40, ___?

Pattern: ×2
Next = 40 × 2 = 80

✅ Answer: 80

🔹 Q6. Average

Q: The average of 6 numbers is 30. What is their total sum?

Solution:
Sum = Average × Count = 30 × 6 = 180

✅ Answer: 180

🔹 Q7. Ratio & Proportion

Q: Divide ₹3000 in the ratio 2:3.

Solution:
Total parts = 2 + 3 = 5
1 part = 3000 / 5 = ₹600
Shares = 2×600 = ₹1200, 3×600 = ₹1800

✅ Answer: ₹1200 and ₹1800

🔹 Q8. Boat & Stream

Q: A boat goes 20 km downstream in 2 hours. Speed of stream = 2 km/h. What is the speed of boat in still water?

Solution:
Downstream speed = 20 / 2 = 10 km/h
Boat speed = 10 – 2 = 8 km/h

✅ Answer: 8 km/h

🔹 Q9. Work & Time

Q: A can do a work in 12 days, B in 18 days. How many days will they take together?

Solution:
1 day work = 1/12 + 1/18 = (3 + 2)/36 = 5/36
Time = 36/5 = 7.2 days

✅ Answer: 7.2 days

🔹 Q10. Percentage

Q: What is 25% of 640?

Solution:
= (25/100) × 640 = 160

✅ Answer: 160

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