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Fundamental Arithmetic Operations

Mathematical Abilities — Paper-I · Official 2026 Coverage

Useful for: SSC CGL

Overview

Tier-II arithmetic combines percentages, ratios, interest, time–work and time–speed in multi-step problems.

Key points

Income–expenditure–savings: income = expenditure + savings; set ratios as multiples.
Relative speed for two trains: add when opposite, subtract when same direction; distance = sum of lengths.
Compound interest for 3 years at 5%: multiply by 1.05³ = 1.157625.
Mixture and partnership use ratio of quantity × price or capital × time.
Use 100 as the base for percentage chains.

Explanation

Write two equations when two ratios are given; eliminate one variable.
For CI with small rates, successive % can replace powers.
Convert km/h to m/s (× 5/18) before using metres.
Check every answer for reasonableness (savings less than income, time positive).

Step by step

Identify the concept and the formula that links the given values.
Solve step by step, keeping units consistent.
Check the answer against the options and by a quick estimate.

Examples

Incomes are in the ratio 3:4 and expenditures 5:7; each saves ₹2,000 → 3x − 5y = 2,000 and 4x − 7y = 2,000 → y = 2,000, x = 4,000 → incomes ₹12,000 and ₹16,000.
Trains of 120 m and 180 m at 54 km/h and 36 km/h move towards each other: relative speed 90 km/h = 25 m/s → time = 300/25 = 12 s.
CI on ₹8,000 at 5% for 3 years: 8,000 × 1.157625 = 9,261 → CI = ₹1,261.

Traps and advanced points

Trap: Using the same multiplier for both ratios.
Trap: Forgetting to add the lengths of both trains.
Trap: Applying SI instead of CI.

Quick revision

Two ratios → two variables.
Sum of lengths for crossing trains.
1.05³ = 1.157625.

Practice MCQs

The value of 20 − 4 × 3 + 6 ÷ 2 is
1. 5
2. 51
3. 27
4. 11
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Answer: (d) 11. Do × and ÷ first: 20 − 12 + 3.
15% of 240 is
1. 40
2. 24
3. 16
4. 36
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Answer: (d) 36. 240 × 15 ÷ 100.
3/8 written as a decimal is
1. 0.83
2. 0.38
3. 0.375
4. 0.0375
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Answer: (c) 0.375. 3 ÷ 8.
The average of the first 10 natural numbers is
1. 10
2. 5
3. 6
4. 5.5
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Answer: (d) 5.5. (1 + 10) ÷ 2.
√1764 equals
1. 44
2. 38
3. 42
4. 48
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Answer: (c) 42. 42 × 42 = 1764.
0.2 × 0.3 equals
1. 0.006
2. 0.6
3. 0.06
4. 6
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Answer: (c) 0.06. Two decimal places in total.

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Notes and questions are written by Kundali IQ for practice. They are not official papers; always check the latest official notification for the syllabus and pattern.