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Proportional Reasoning-1 Class 8 Maths Worksheet with Answers Chapter 7

Updated:7 Mins Read

Ganita Prakash Part-I, Grade 8, Textbook of Mathematics – Here is another very important chapter from the NCERT Class 8 book “Proportional Reasoning-1.” In this chapter, you are going to solve worksheet questions related to the following topics –

  • Ratios and simplification
  • Equivalent ratios check
  • Proportion and cross-multiply
  • Unit rate comparisons
  • Direct proportion problems

Basic, Standard, Advance, and HOTS are the 4 sections in this worksheet. In section 2 below we have the answers.

Class 8 Maths Worksheet – Chapter 7: Proportional Reasoning-1

Basic

  1. A rectangle has width 60 mm and height 40 mm.

    1. Write the ratio width : height.
    2. Write it in simplest form.
  2. Reduce each ratio to simplest form:

    1. 30 : 20
    2. 90 : 60
    3. 40 : 20
  3. Are these ratios proportional? (Write Yes/No)

    1. 3 : 4 and 72 : 96
    2. 2 : 3 and 8 : 15
    3. 5 : 7 and 15 : 21
  4. Fill the missing term to make the ratios proportional:

    1. 14 : 21 :: 28 : ____
    2. 14 : 21 :: 6 : ____
    3. 14 : 21 :: 2 : ____
  5. A recipe uses 6 cups of water for 10 spoons of sugar.
    How many spoons of sugar are needed for 18 cups of water (same sweetness)?
  6. Write 3 ratios proportional to 4 : 9.

Standard

  1. Check if the statement is true:
    4 : 7 :: 12 : 21
  2. Compare two walls for “same strength” using ratios:
    Wall A: 60 ft uses 3 bags of cement
    Wall B: 40 ft uses 2 bags of cement
    Are the ratios proportional? (Yes/No)
  3. Cross-multiplication:
    If a : b :: c : d, then ________ = ________
  4. Rule of Three:
    A car travels 90 km in 150 minutes. How far will it travel in 240 minutes (same speed)?
  5. Tea price comparison:
    Himachal: 200 g costs ₹200
    Meghalaya: 1 kg costs ₹800
    Which is more expensive per kg?
  6. Strong / Regular / Light coffee:
    Regular coffee uses 15 mL decoction with 35 mL milk.
    Decide if each mix is Stronger or Lighter than regular:

    1. 20 mL decoction, 30 mL milk
    2. 10 mL decoction, 40 mL milk
    3. 24 mL decoction, 56 mL milk

Advance

  1. A school meal uses 15 kg rice for 120 students.
    How much rice is needed for 80 students (same serving)?
  2. Divide ₹4500 in the ratio 2 : 3.
  3. A solution has acid : water = 1 : 5.
    In 240 mL solution, find acid and water (in mL).
  4. Paint mix:
    Blue : Yellow = 3 : 5 gives 40 mL green paint.
    Find how much Blue and Yellow are used.
  5. Mixture problem:
    40 kg mixture has sand : cement = 3 : 1.
    How many kg cement must be added to make sand : cement = 5 : 2?
  6. Unit conversion:
    A tap fills 500 mL in 15 s. How long to fill 10 L?

HOTS

  1. Trick check:
    Puneeth’s father rides 50 km/h and takes 2 hours.
    If speed becomes 75 km/h, time will be (More / Less)?
    Explain in 1–2 lines why this is not solved by writing 50 : 2 :: 75 : x.
  2. Market table thinking:
    Shampoo sizes: 6 mL costs ₹2, 180 mL costs ₹154.
    Are “volume : volume” proportional to “price : price”? (Yes/No)
    Give one reason.
  3. Land manure problem:
    Recommended: 10 tonnes manure per acre.
    Plot size: 200 ft × 500 ft.
    How many tonnes manure needed?
    (Use 1 acre = 43,560 sq ft.)
  4. Crowded city idea:
    Delhi area 1484 sq km, population 30 million
    Mumbai area 550 sq km, population 20 million
    Which is more crowded? Show using population per sq km (approx.).
  5. Split coins:
    Share 42 counters in the ratio 4 : 3.
    Also write each share as a fraction of the total.
  6. Alloy cost mini-project:
    A ₹10 coin has copper : nickel = 3 : 1, total mass 7.74 g.
    If copper costs ₹906/kg and nickel costs ₹1341/kg, find the cost of metals in one coin (approx.).

Answer Key

Basic – Answers

    1. Ans: 60 : 40
    2. Ans: 3 : 2
      Hint: Divide both terms by 20.
    1. Ans: 30 : 20 = 3 : 2
    2. Ans: 90 : 60 = 3 : 2
    3. Ans: 40 : 20 = 2 : 1
    1. Ans: Yes (72:96 → 3:4)
    2. Ans: No (2:3 ≠ 8:15)
    3. Ans: Yes (15:21 → 5:7)
    1. Ans: 42
      Hint: Factor is 2.
    2. Ans: 9
      Hint: 14→6 is ×(3/7), so 21→9 is ×(3/7).
    3. Ans: 3
      Hint: Divide both by 7.
  5. Ans: 30 spoons
    Hint: 18 is 3 times 6, so sugar is 3 times 10.
  6. Ans: Example answers: 4:9, 8:18, 12:27
    Hint: Multiply both terms by same number.

Standard – Answers

  1. Ans: True
    Hint: 12:21 simplifies to 4:7.
  2. Ans: Yes
    60:3 = 20:1 and 40:2 = 20:1
    Hint: Compare simplest forms.
  3. Ans: a×d = b×c
    Hint: Cross-multiply.
  4. Ans: 144 km
    Work: 150:90 :: 240:x ⇒ 150x = 240×90 ⇒ x = (240×90)/150 = 144
  5. Ans: Himachal is more expensive.
    Work: 200 g costs 200, so 1000 g costs 5×200 = ₹1000; Meghalaya is ₹800/kg.
    1. Ans: Stronger
      Hint: Decoction fraction increases.
    2. Ans: Lighter
      Hint: More milk per decoction.
    3. Ans: Same as regular
      Work: 24:56 simplifies to 3:7, and 15:35 also simplifies to 3:7.

Advance – Answers

  1. Ans: 10 kg
    Work: 120:15 :: 80:x ⇒ 120x = 80×15 ⇒ x = 10
  2. Ans: ₹1800 and ₹2700
    Hint: Total parts = 5, one part = 4500/5 = 900.
  3. Ans: Acid = 40 mL, Water = 200 mL
    Hint: Total parts = 6, one part = 240/6 = 40.
  4. Ans: Blue = 15 mL, Yellow = 25 mL
    Hint: Total parts = 8, one part = 40/8 = 5.
  5. Ans: Add 2 kg cement
    Work: 40 kg with 3:1 → sand 30, cement 10.
    New ratio 5:2 with sand 30 ⇒ cement = (2/5)×30 = 12, so add 2.
  6. Ans: 300 s (5 minutes)
    Work: 10 L = 10,000 mL. Time = (10,000/500)×15 = 20×15 = 300 s.

HOTS – Answers

  1. Ans: Less time
    Reason: Time is inversely related to speed for fixed distance, so it cannot be modelled by direct proportion 50:2 :: 75:x.
  2. Ans: No
    Reason: Price does not scale by the same factor as volume here (bigger bottles may be cheaper per mL).
  3. Ans: About 22.96 tonnes (approx.)
    Work: Area = 200×500 = 100,000 sq ft.
    Acres = 100,000/43,560 = 2.2957.
    Manure = 10×2.2957 = 22.96 tonnes.
  4. Ans: Mumbai is more crowded (approx.)
    Work: Delhi: 30,000,000/1484 = 20,200 per sq km.
    Mumbai: 20,000,000/550 = 36,400 per sq km.
  5. Ans: Shares: 24 and 18
    Fractions: 24/42 = 4/7 and 18/42 = 3/7
  6. Ans: About ₹0.009 (less than 1 paisa, approx.)
    Work: Copper mass = (3/4)×7.74 = 5.805 g; Nickel mass = (1/4)×7.74 = 1.935 g.
    Copper cost per g = 906/1000 = ₹0.906; Nickel cost per g = 1341/1000 = ₹1.341 (per gram if per kg)
    Convert correctly: ₹906 per kg ⇒ ₹0.906 per gram; ₹1341 per kg ⇒ ₹1.341 per gram.
    Cost = 5.805×0.906 + 1.935×1.341 = 5.26 + 2.60 = ₹7.86
    Note: This is the raw metal cost estimate (ignores manufacturing).

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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