RD Sharma Solutions for Class 7 Maths Chapter 9: Ratio and Proportion

Overview

• RD Sharma solutions for this chapter are designed to help students achieve excellent marks by providing detailed explanations and solutions for each problem.
• The chapter discusses fundamental concepts such as ratio, proportion, and various related topics.

Key Concepts

• Ratio: A fraction showing how many times one quantity is to another, applicable to quantities of the same kind and units.
  • Simplest Form: Reduce ratios to their simplest form.
  • Comparison: Methods to compare different ratios.
  • Equivalent Ratios: Ratios that represent the same relationship.
• Proportion: The equality of two ratios.
  • Mean Proportional: A concept discussed within the chapter.

Exercises and Solutions Summary

Exercise 9.1

• Problem 1: Given x: y = 3:5, solve for the ratio of 3x + 4y to 8x + 5y.
  • Solution: Ratio is 29:49.
• Problem 2: Given x: y = 8:9, find the ratio of (7x - 4y) to (3x + 2y).
  • Solution: Ratio is 10:21.
• Problem 3: Calculate numbers from a ratio of 6:13 with an L.C.M of 312.
  • Solution: Numbers are 24 and 52.
• Problem 4: Two numbers are in a ratio of 3:5, with 8 added to each, the new ratio is 2:3.
  • Solution: Numbers are 24 and 40.
• Problem 5: Determine what should be added to 7:13 to make it 2:3.
  • Solution: Add 5.
• Problem 6: Three numbers in ratio 2:3:5 with a sum of 800.
  • Solution: Numbers are 160, 240, and 400.
• Problem 7: Ages in ratio 5:7, 18 years ago in ratio 8:13.
  • Solution: Present ages are 50 and 70 years.
• Problem 8: Numbers in ratio 7:11, adding 7 changes ratio to 2:3.
  • Solution: Numbers are 49 and 77.
• Problem 9: Numbers in ratio 2:7 with a sum of 810.
  • Solution: Numbers are 180 and 630.
• Problem 10: Divide Rs 1350 in ratio 2:3.
  • Solution: Rs. 540 and Rs. 810.
• Problem 11: Divide Rs 2000 among P, Q, R in ratio 2:3:5.
  • Solution: Rs. 400, Rs. 600, Rs. 1000.
• Problem 12: Boys to girls ratio 7:4 in a school of 550.
  • Solution: 350 boys, 200 girls.
• Problem 13: Income to savings ratio 7:2, with savings Rs. 500.
  • Solution: Income is Rs. 1750, expenditure Rs. 1250.
• Problem 14: Triangle sides in ratio 1:2:3 with perimeter 36 cm.
  • Solution: Sides are 6 cm, 12 cm, 18 cm.
• Problem 15: Divide Rs 5500 in ratio 2:3.
  • Solution: Rs. 2200 and Rs. 3300.
• Problem 16: Zinc to copper ratio 7:9 in an alloy with copper 11.7 kg.
  • Solution: Zinc weight is 9.10 kg.
• Problem 17: Consequent is 40 in ratio 7:8, find antecedent.
  • Solution: Antecedent is 35.
• Problem 18: Divide Rs 351 in ratio 2:7.
  • Solution: Rs. 78 and Rs. 273.
• Problem 19: Pencil to ball pen price ratio if pencil costs Rs.16/score and pen costs Rs.8.40/dozen.
  • Solution: Ratio is 8:7.
• Problem 20: In a class of 42, one in six fails.
  • Solution: 35 pass.

Exercise 9.2

• Comparative Analysis of Ratios: Determine which ratios are larger among given pairs.
  • Solutions involve converting to a common denominator to compare.
• Equivalent Ratios: Find equivalent ratios for given fractions.
• Blanks Completion: Complete given fractions to form equivalent ratios.

Exercise 9.3

• Proportions: Identify sets of numbers in proportion.
  • Uses cross multiplication to verify proportions.
• Find x in Proportions: Solve for x in given proportions using cross multiplication.
• Income and Expenditure Problems: Use ratios to determine savings, expenditures, and incomes.
• Scale Problems: Conversion using given scales to determine actual distances.
• Height Problems: Use shadow length ratios to calculate heights of objects.

Conclusion

• The solutions provide detailed steps for each problem, fostering better understanding and problem-solving skills in students.
• Concepts of ratio and proportion are crucial for further mathematical applications and real-world problems.