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AFCAT Mathematics — practice by topic

Browse 13 questions across 6 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Mensuration: Surface Areas & Volumes (5)LCM and HCF (4)Elementary Algebra (1)Elementary Statistics (1)Ratio and Proportion (1)Time, Speed and Distance (1)

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A man covers half of a journey at $40$ km/hr and the other half at $60$ km/hr. Find his average speed for the whole journey.Read the answer and worked solution →Find the area of a square whose side is $7$ cm.Read the answer and worked solution →A rectangle has area $48$ cm² and breadth $6$ cm. Find its length.Read the answer and worked solution →Find the area of an equilateral triangle whose side is $6$ cm.Read the answer and worked solution →

Worked practice questions

A man covers half of a journey at $40$ km/hr and the other half at $60$ km/hr. Find his average speed for the whole journey.

  1. $45$ km/hr
  2. $48$ km/hr
  3. $50$ km/hr
  4. $52$ km/hr
Show answer and solution

Correct answer: B. $48$ km/hr

For equal distances, average speed is the harmonic mean: $\dfrac{2xy}{x+y} = \dfrac{2 \times 40 \times 60}{100} = \dfrac{4800}{100} = 48$ km/hr. Option C ($50$, the arithmetic mean) applies only when *time* is split equally, not distance.

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Find the area of a square whose side is $7$ cm.

  1. $28$ cm²
  2. $42$ cm²
  3. $49$ cm²
  4. $56$ cm²
Show answer and solution

Correct answer: C. $49$ cm²

Area of a square $= \text{side}^2 = 7^2 = 49$ cm².

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A rectangle has area $48$ cm² and breadth $6$ cm. Find its length.

  1. $6$ cm
  2. $8$ cm
  3. $10$ cm
  4. $12$ cm
Show answer and solution

Correct answer: B. $8$ cm

Length $= \dfrac{\text{Area}}{\text{Breadth}} = \dfrac{48}{6} = 8$ cm.

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