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Arithmetic

Mathematics

Useful for: OSSC RHT — Regular High School Teacher, UPSC CDS, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Science, OSSC Mathematics, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts, OSSSC Govt TGT Science — CBZ

and 3 more exams

OSSSC Govt TGT Science — PCM, SSB Lecturer (Degree Colleges), SSB TGT PCM

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Overview

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

  1. Identify the concept and the formula that links the given values.
  2. Solve step by step, keeping units consistent.
  3. 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

  1. From the perspective of definition and scope, which one of the following statements about Arithmetic is correct?

    1. Arithmetic is unrelated to institutions, processes or real-world applications.
    2. Arithmetic has no exceptions or limitations in exam analysis.
    3. Arithmetic in CDS is elementary-mathematics level and rewards speed with conceptual accuracy.
    4. Do not skip unit or sign checks in Arithmetic.

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    Answer: (c) Arithmetic in CDS is elementary-mathematics level and rewards speed with conceptual accuracy.. Arithmetic in CDS is elementary-mathematics level and rewards speed with conceptual accuracy.

  2. Consider the following statements on Arithmetic and Trigonometry, focusing on definition and scope: 1. Do not skip unit or sign checks in Arithmetic. 2. Do not apply a memorized Trigonometry formula without checking its conditions. Which of the statements given above is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2

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    Answer: (d) Neither 1 nor 2. Neither statement is correct; both are common misconceptions.

  3. Which option best connects the definition and scope dimension of Arithmetic with its broader exam relevance?

    1. Arithmetic can be understood without any mechanism, limitation or exception.
    2. Write the relevant Arithmetic relation before calculation. Also, Check signs, units and approximation before marking.
    3. Do not skip unit or sign checks in Arithmetic.
    4. Every statement about Arithmetic is absolute and context-free.

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    Answer: (b) Write the relevant Arithmetic relation before calculation. Also, Check signs, units and approximation before marking.. Write the relevant Arithmetic relation before calculation. Also, Check signs, units and approximation before marking.

  4. Compound interest for 3 years at 5% multiplies the principal by —

    1. 1.157625
    2. 1.1025
    3. 1.05
    4. 1.15

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    Answer: (a) 1.157625. 1.05³ = 1.157625.

  5. For percentage chains, a convenient base value is —

    1. 1,000
    2. 1
    3. 10
    4. 100

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    Answer: (d) 100. Using 100 simplifies percentages.

  6. Income ₹50,000 and expenditure ₹42,000. Savings are —

    1. ₹6,000
    2. ₹8,000
    3. ₹9,000
    4. ₹92,000

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    Answer: (b) ₹8,000. Income = expenditure + savings.

  7. Two trains 100 m and 150 m long move towards each other at 10 m/s and 15 m/s. Time to cross —

    1. 5 s
    2. 10 s
    3. 25 s
    4. 50 s

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    Answer: (b) 10 s. 250/(10 + 15) = 10 s.

  8. In partnership, profit is shared in the ratio of —

    1. time only
    2. age
    3. capital only
    4. capital × time

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    Answer: (d) capital × time. Capital × time.

  9. A price rises 10% and then 10%. Net increase —

    1. 19%
    2. 22%
    3. 20%
    4. 21%

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    Answer: (d) 21%. 10 + 10 + 1 = 21%.

  10. Simple interest on ₹2,000 at 5% for 3 years is —

    1. ₹200
    2. ₹300
    3. ₹350
    4. ₹150

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    Answer: (b) ₹300. 2,000 × 5 × 3/100 = 300.

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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.