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About Unitary Method — Class 6 ICSE

Solve problems using unitary method including time, distance, and work applications. This topic is part of the ICSE Class 6 mathematics syllabus (chapter: Chapter 13). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Unitary Method

  • Introduction to the Unitary Method
  • Direct Proportion and the Unitary Method
  • Unitary Method for Time and Distance
  • Unitary Method in Simple Work Applications
  • Summary, Connections, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Unitary Method — solved examples for Class 6 ICSE

Example 1easy

If 5 pencils cost Rs 20, what is the cost of 1 pencil?
  1. A)Rs 4
  2. B)Rs 5
  3. C)Rs 10
  4. D)Rs 2

Step-by-step solution

  1. Cost of 5 pencils = Rs 20
  2. Cost of 1 pencil = Total cost / Number of pencils
    20/5=Rs420 / 5 = Rs 4

Answer: Rs 4

Example 2medium

If 15 workers can complete a task in 12 days, how many days will 20 workers take to complete the same task?
  1. A)9 days
  2. B)10 days
  3. C)8 days
  4. D)15 days

Step-by-step solution

  1. Total work = 15 x 12 = 180 worker-days
  2. Days for 20 workers:
    180/20=9days180 / 20 = 9 days

Answer: 9 days

Example 3hard

If 24 workers can build a bridge in 15 days working 8 hours a day, how many days will 16 workers take working 10 hours a day?
  1. A)18 days
  2. B)20 days
  3. C)15 days
  4. D)24 days

Step-by-step solution

  1. Total work = 24 x 15 x 8 = 2880 worker-hours
  2. Days for 16 workers at 10 hrs/day:
    2880/(16x10)=2880/160=18days2880 / (16 x 10) = 2880 / 160 = 18 days

Answer: 18 days

Practice questions on Unitary Method

  1. Q1.easy

    If 8 notebooks cost Rs 96, what is the cost of 1 notebook?
    1. A)Rs 12
    2. B)Rs 8
    3. C)Rs 16
    4. D)Rs 10
    Show answer

    Answer: Rs 12

    Hint: Divide Rs 96 by 8 to find the cost of one notebook.

  2. Q2.easy

    If 3 kg of rice costs Rs 150, what is the cost of 1 kg?
    1. A)Rs 50
    2. B)Rs 45
    3. C)Rs 30
    4. D)Rs 75
    Show answer

    Answer: Rs 50

    Hint: Divide the total cost by the weight in kg.

  3. Q3.easy

    If 1 pen costs Rs 15, what is the cost of 7 pens?
    1. A)Rs 105
    2. B)Rs 90
    3. C)Rs 75
    4. D)Rs 120
    Show answer

    Answer: Rs 105

    Hint: Multiply the cost of 1 pen by the number of pens.

  4. Q4.medium

    A shopkeeper sells 3.5 kg of dal for Rs 315. What is the cost of 5 kg of dal?
    1. A)Rs 450
    2. B)Rs 400
    3. C)Rs 500
    4. D)Rs 350
    Show answer

    Answer: Rs 450

    Hint: Find the cost of 1 kg by dividing 315 by 3.5.

  5. Q5.medium

    A car uses 8 litres of petrol to travel 96 km. How many litres are needed to travel 240 km?
    1. A)20 litres
    2. B)24 litres
    3. C)18 litres
    4. D)16 litres
    Show answer

    Answer: 20 litres

    Hint: Find how many km the car travels per litre, then work backwards.

  6. Q6.medium

    If 18 men can dig a trench in 10 days, how many men are needed to dig it in 6 days?
    1. A)30 men
    2. B)24 men
    3. C)36 men
    4. D)27 men
    Show answer

    Answer: 30 men

    Hint: This is inverse variation. Find total man-days, then divide by 6.

  7. Q7.hard

    A train covers 360 km in 4 hours. Another train covers 480 km in 6 hours. What is the difference in their speeds?
    1. A)10 km/hr
    2. B)20 km/hr
    3. C)15 km/hr
    4. D)5 km/hr
    Show answer

    Answer: 10 km/hr

    Hint: Find the speed of each train separately, then subtract.

  8. Q8.hard

    If 12 cows eat 756 kg of fodder in 7 days, how much fodder will 15 cows eat in 10 days?
    1. A)1350 kg
    2. B)1260 kg
    3. C)1500 kg
    4. D)1080 kg
    Show answer

    Answer: 1350 kg

    Hint: Find the fodder eaten by 1 cow in 1 day first.

  9. Q9.hard

    Rajesh cycles at 12 km/hr and reaches school in 25 minutes. If he wants to reach in 20 minutes, at what speed should he cycle?
    1. A)15 km/hr
    2. B)14 km/hr
    3. C)16 km/hr
    4. D)18 km/hr
    Show answer

    Answer: 15 km/hr

    Hint: Distance is fixed. Use speed x time = constant (with same units).

These are 9 of the 60 questions available for Unitary Method. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.