Ratios Problem-Solving Tips for Income and Expenditure
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Questions and Answers

What is the purpose of using the cross-multiplication method in ratio problems?

  • To find the percentage of income saved by an individual
  • To find the total income of two individuals
  • To determine the savings of one individual
  • To find the expenditure ratio from the income ratio (correct)

    • Ajay and Veeru have an income ratio of 5:4 and an expenditure ratio of 6:5. What can be inferred about Ajay's income?

  • Ajay's income is ₹7
  • Ajay's income is ₹5
  • Ajay's income cannot be determined (correct)
  • Ajay's income is ₹6

    • In a scenario where the ratio of tanks to planes in an army is given, what can be computed using the cross-multiplication method?

  • The ratio of tanks to planes after the battle (correct)
  • The number of tanks destroyed during the battle
  • The number of planes destroyed during the battle
  • The initial number of tanks and planes

    • What is the final ratio of students who've passed and failed after some students join and leave?

    <p>2:1</p> Signup and view all the answers

    What is the ratio of passed students to failed students if the ratio changes from 5:4 to 7:5 after some students join?

    <p>The ratio changes to 7:5</p> Signup and view all the answers

    If there's a change in the number of officers and no change in the number of assistants, what should remain the same?

    <p>The ratio of officers to assistants</p> Signup and view all the answers

    What is the cross-multiplication method used for in ratio problems involving incomes and expenditures?

    <p>To find the expenditure ratio from the income ratio</p> Signup and view all the answers

    What is the ratio of Rs. 10, Rs. 2, and Rs. 1 coins in the bag?

    <p>10:5:2</p> Signup and view all the answers

    What is the first step in using the cross-multiplication method in a problem involving Ajay and Veeru's incomes?

    <p>Find the expenditure ratio from the income ratio</p> Signup and view all the answers

    If the total value of coins in the bag is Rs. 87 and the ratio of Rs. 10, Rs. 5, Rs. 2, and Rs. 1 coins is 10:5:2:1, what is the value of Rs. 1 coins?

    <p>Rs. 40</p> Signup and view all the answers

    What is the total value of all notes in the bag?

    <p>Rs. 1235</p> Signup and view all the answers

    What is emphasized in the given series of mathematical problem-solving scenarios?

    <p>Understanding value ratios and calculating total values</p> Signup and view all the answers

    Study Notes

    Ratios Problem-Solving Tips

    • In the problem where the ratio of incomes of Ajay and Veeru is 5:4 and their expenses 6:5, it's possible to use the cross-multiplication method for solving such questions.
    • In this scenario, from the income, the savings will be subtracted to get the final ratio which reflects the expenditure
    • For each question involving cross-multiplication, the final ratio should always be equivalent to the expenditure in the problem.
    • The percentage of income saved by Ajay then can be found by subtracting Ajay's income from his savings.

    Cross-Multiplication Method in Ratios

    • In, a question where Ajay and Bina's income ratio is 5:4 and their expenditure ratio is 6:5, the cross-multiplication method can be employed.
    • Assume that Ajay's saving is ₹7 and Bina's saving is ₹5, then their expenditures can be determined by subtracting their savings from their income.

    Ratios in Military Context

    • In a scenario where there's a ratio of tanks to planes in an army before a battle, and the number of tanks and planes destroyed during the battle, the remaining ratio of tanks to planes after the battle can be computed via cross-multiplication.

    Ratios in the Context of Students and Examinations

    • The ratio of students who've passed or failed an exam, and the changes to this ratio after some students join or leave, can be solved using the cross-multiplication method.
    • For instance, consider the ratio of passed students to failed students before an exam was 5:4. Then, after some students join and leave, this ratio changes to 2:1. The total number of students after the changes can then be determined through cross-multiplication, with the final list giving the number of students who've passed and failed after the changes.

    Direct and Reverse Calculation in Ratios

    • When a question involves direct and reverse calculations, like an officer and assistant ratio, the reverse calculation method can help solve the problem.
    • If there's a change in the number of officers and no change in the number of assistants, the ratio of officers to assistants should remain the same. By setting those two ratios equal to each other, it's possible to calculate the missing value.### Bag with Coins
    • Bag contains coins of Rs. 1, Rs. 2, and Rs. 5 denominations
    • If Rs. 1 coins are 10, Rs. 2 coins are 5, and Rs. 5 coins are 2, then the ratio of their quantities is 10:5:2
    • Total value of coins in the bag is Rs. 87
    • The quantity of Rs. 1 coins is asked
    • The value ratio of notes Rs. 10: Rs. 20 is 118:10:20
    • Rs. 10 coins are 3 times the quantity of Rs. 5 coins, making a ratio of 15:5
    • If there are Rs. 10 notes in the bag, and their total value is 87, then the Rs. 10 coins will be 45
    • The bag has a value of 87, and the ratio of Rs. 10 notes is 5, the ratio of Rs. 20 notes is 3, making a total value of Rs. 87
    • The value ratio of coins was Rs. 10: Rs. 5: Rs. 2: Rs. 1, which equates to 10:5:2:1
    • The Rs. 2 and Rs. 10 notes were three times the Rs. 1 notes, creating a total of 72 units of coins
    • If each Rs. 10 note was worth 10 units, then the total worth of coins in the bag would be 720 units
    • The Rs. 1 coins were Rs. 40, Rs. 5 coins were Rs. 15, Rs. 2 coins were Rs. 7
    • The Rs. 5 coins were Rs. 55, making the total value of those coins Rs. 275
    • With 40 Rs. 10 notes, the total value would be Rs. 400
    • With 28 Rs. 20 notes, the total value would be Rs. 560
    • Therefore, the total value of all coins would be Rs. 1235
    • The bag contains 40 Rs. 10 notes, with a total value of Rs. 400
    • The bag also contains 28 Rs. 20 notes, with a total value of Rs. 560
    • Therefore, the total value of all notes in the bag is Rs. 1235

    Conclusion

    • The text encompasses a series of mathematical problem-solving scenarios related to coin values in a bag, emphasizing the importance of understanding value ratios and calculating total values effectively.

    Ratios Problem-Solving Tips

    • Use cross-multiplication method to solve ratio problems involving income and expenses.

    Cross-Multiplication Method in Ratios

    • Assume savings and expenditures to find ratios of incomes and expenses.

    Ratios in Military Context

    • Calculate remaining ratio of tanks to planes after a battle using cross-multiplication.

    Ratios in the Context of Students and Examinations

    • Use cross-multiplication to find total number of students after changes in the ratio of passed to failed students.

    Direct and Reverse Calculation in Ratios

    • Use reverse calculation method to solve ratio problems involving changes in the number of officers and assistants.

    Bag with Coins

    • Calculate the ratio of coin quantities: Rs. 1 coins (10), Rs. 2 coins (5), and Rs. 5 coins (2).
    • Total value of coins in the bag is Rs. 87.
    • Quantity of Rs. 1 coins is asked.
    • Value ratio of notes: Rs. 10: Rs. 20 = 118:10:20.
    • Total value of Rs. 10 notes is 45.
    • Bag has a total value of 87 with ratio of Rs. 10 notes = 5, Rs. 20 notes = 3.
    • Value ratio of coins: Rs. 10: Rs. 5: Rs. 2: Rs. 1 = 10:5:2:1.
    • Rs. 2 and Rs. 10 notes are three times the quantity of Rs. 1 notes, making a total of 72 units of coins.
    • Total worth of coins in the bag is 720 units.
    • Rs. 1 coins are 40 units, Rs. 5 coins are 15 units, Rs. 2 coins are 7 units.
    • Rs. 5 coins are 55 units, making the total value of those coins 275 units.
    • Total value of all coins is 1235 units.
    • Bag contains 40 Rs. 10 notes, with a total value of Rs. 400.
    • Bag also contains 28 Rs. 20 notes, with a total value of Rs. 560.

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    Description

    Get tips on solving ratio problems involving income and expenditure, including using the cross-multiplication method. Learn how to find the final ratio and percentage of income saved.

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