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Proportional Reasoning–2 Class 8 Maths Worksheet with Answers Chapter 3

Updated:6 Mins Read

Ganita Prakash Part-II, Grade 8, Textbook of Mathematics – This is Chapter 3 from Ganita Prakash Part-II from NCERT Maths book. The chapter is “Proportional Reasoning–2”. You might have already csolved the questions in the part 1. This chapter is extension for that chapter. In the worksheet below, following topics are covered –

  • Scale and ratio
  • Division in ratio
  • Pie chart angles
  • Inverse proportion problems
  • Work time comparisons

The worksheet is divided into 4 parts – Basic, Standard, Advance, and HOTS. The answers for the below section is also there at the end.

Class 8 Maths Worksheet – Proportional Reasoning–2

Basic

  1. Check proportionality using cross-multiplication:

    1. 6 : 3 and 4 : 2
    2. 14 : 21 and 28 : 42
    3. 3 : 5 and 21 : 30
  2. A map has RF 1 : 60,00,000.

    1. What actual distance does 1 cm represent (in km)?
    2. What actual distance does 5 cm represent (in km)?
  3. Viswanath’s spice mix ratio is 8 : 4 : 2 : 1.
    Puneet has only 2 red chillies.
    Write the new proportional ratio.
  4. Divide 12 in the ratio 2 : 1.
  5. Paint is mixed in the ratio Red : Blue : White = 2 : 3 : 5.
    If total paint needed is 50 mL, find mL of each colour.
  6. Constructing triangle angles:
    Angles are in the ratio 1 : 3 : 5.
    Find the three angles (in degrees).

Standard

  1. A cricket session ratio is Warm-up/Cool-down : Batting : Bowling : Fielding = 3 : 4 : 3 : 5.
    Total session time is 150 minutes.
    Find time (in minutes) for each activity.
  2. A library has books in ratio Odiya : Hindi : English = 3 : 2 : 1.
    If Odiya books are 288, find Hindi and English books.
  3. A person has 100 coins in ratio
    ₹10 coins : ₹5 coins : ₹2 coins : ₹1 coins = 4 : 3 : 2 : 1.
    Find total money.
  4. Grade counts are A=12, B=10, C=8, D=6, E=4 (total 40 students).
    Find the central angle for each grade in a pie chart.
  5. In a group of 360 people:
    Summer=90, Rainy=120, Winter=150.
    Find the pie chart angle for each season.
  6. Which pairs are in inverse proportion? Write Yes/No.

    1. Number of taps and time to fill a tank
    2. Number of painters and days to paint a wall
    3. Distance travelled and petrol in tank (fixed mileage)
    4. Speed and time for fixed distance
    5. Cloth length and price (fixed rate)
    6. Pages in a book and reading time (fixed speed)

Advance

  1. 20 workers finish a job in 4 days.
    How many days will 10 workers take for the same job?
  2. 2 pumps fill a tank in 18 hours.
    How long will 4 similar pumps take?
  3. Food provisions feed 80 students for 15 days.
    If 100 students eat, for how many days will food last?
  4. A pump fills 2 identical tanks in 6 hours.
    How long will it take to fill 5 such tanks with the same pump?
  5. 25 rows with 12 chairs each are rearranged into rows of 20 chairs each.
    How many rows will be formed?
  6. A school has 8 periods of 45 minutes each.
    If it changes to 9 periods but total school time stays the same, find the new period duration.

HOTS

  1. Crowded city check:
    Delhi area 1484 sq km, population 30 million.
    Mumbai area 550 sq km, population 20 million.
    Which is more crowded? Use population per sq km (approx.).
  2. A transport pie chart has angles:
    Walk 90°, Cycle 60°, Bus 120°, Two-wheeler 60°, Car 30°.
    If 18 children travel by car, find:

    1. Total children in survey
    2. Number of children who travel by bus
  3. A small pump fills a tank in 3 hours.
    A large pump fills the same tank in 2 hours.
    If both pumps run together, how long will they take?
  4. A factory uses 42 machines to finish work in 63 days.
    How many machines are needed to finish the same work in 54 days?
  5. If 24 pencils cost ₹120, how much will 20 such pencils cost?
  6. A car travels at 60 km/h for 2 hours.
    How long will it take to cover the same distance at 80 km/h?

Answer Key

Basic – Answers

    1. Yes
    2. Yes
    3. No

    Hint: Check a×d and b×c.

    1. 60 km
    2. 300 km

    Hint: 60,00,000 cm = 60 km, so scale linearly.

  3. 4 : 2 : 1 : 0.5
    Hint: Red chillies become half, so all terms become half.
  4. 8 and 4
    Hint: Total parts = 3, one part = 12/3.
  5. Red 10 mL, Blue 15 mL, White 25 mL
    Hint: Total parts = 10, one part = 50/10.
  6. 20°, 60°, 100°
    Hint: Total ratio = 9 parts, each part = 180°/9.

Standard – Answers

  1. Warm-up/Cool-down 30, Batting 40, Bowling 30, Fielding 50 (minutes)
    Hint: Total parts = 15, one part = 150/15.
  2. Hindi 192, English 96
    Hint: 3 parts = 288, so 1 part = 96.
  3. ₹600
    Hint: Coins are 40,30,20,10 respectively.
  4. A 108°, B 90°, C 72°, D 54°, E 36°
    Hint: Angle = (students/40)×360.
  5. Summer 90°, Rainy 120°, Winter 150°
    Hint: Angle = (count/360)×360 = count degrees here.
    1. Yes
    2. Yes
    3. No
    4. Yes
    5. No
    6. No

    Hint: In inverse proportion, product stays constant.

Advance – Answers

  1. 8 days
    Hint: Workers×Days = constant.
  2. 9 hours
    Hint: Pumps×Time = constant.
  3. 12 days
    Hint: Students×Days = constant.
  4. 15 hours
    Hint: One tank takes 3 hours, so multiply by 5.
  5. 15 rows
    Hint: Total chairs = 25×12 = 300, then 300/20.
  6. 40 minutes
    Hint: Total time = 8×45 = 360 minutes, then 360/9.

HOTS – Answers

  1. Mumbai is more crowded
    Work: Delhi ≈ 30,000,000/1484 ≈ 20,200 per sq km
    Mumbai ≈ 20,000,000/550 ≈ 36,400 per sq km
    1. Total children = 216
    2. Bus travellers = 72

    Hint: Car is 30° out of 360°, so it is 1/12 of total.

  3. 6/5 hours = 1 hour 12 minutes
    Hint: Add rates: 1/3 + 1/2 = 5/6 tank per hour.
  4. 49 machines
    Hint: Machines×Days = constant, so 42×63 = x×54.
  5. ₹100
    Hint: Unit cost = 120/24 = 5 per pencil.
  6. 1.5 hours
    Hint: Distance is same: 60×2 = 120 km, then 120/80.

Worksheet From Other Chapters

Ganita Prakash Part-I

Ganita Prakash Part-II

Amit, a BE in Mechanical Engineering, is a math enthusiast dedicated to making math fun and accessible for kids in classes 1 to 10. With a knack for simplifying complex concepts, Amit offers easy-to-understand solutions, fostering a love for math in young minds across India.

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