Ratio, Proportion


  1. The income of A and B are in the ratio 2 : 3 and their expenditures are in the ratio 1 : 2. If each saves ₹ 24,000, find A’s income.









  1. View Hint View Answer Discuss in Forum

    Let the income of A and B be ₹ 2x and ₹ 3x. and their expenditures be ₹ y and ₹ 2y respectively.
    ∴  2x – y = 24000      ...(i)
    and 3x – 2y = 24000      ...(ii)
    By equation (i) × 2 – (ii),
    4x – 2y – 3x + 2y = 24000
    ⇒  x = 24000
    ∴  A’s income = 2 × 24000
    = ₹ 48000

    Correct Option: D

    Let the income of A and B be ₹ 2x and ₹ 3x. and their expenditures be ₹ y and ₹ 2y respectively.
    ∴  2x – y = 24000      ...(i)
    and 3x – 2y = 24000      ...(ii)
    By equation (i) × 2 – (ii),
    4x – 2y – 3x + 2y = 24000
    ⇒  x = 24000
    ∴  A’s income = 2 × 24000
    = ₹ 48000


  1. The ratio of the incomes of A and B as well as of B and C is 3 : 2. If one third of A’s income exceeds one fourth of C's income by ₹ 1000, what is B’s income in ?









  1. View Hint View Answer Discuss in Forum

    A : B = 3 : 2 = 9 : 6
    B : C = 3 : 2 = 6 : 4
    ∴  A : B : C = 9 : 6 : 4

    ∴ 
    9x
    4x
    = 1000
    34

    ⇒  3x – x = 1000
    ⇒  2x = 1000
    ⇒  x = 500
    ∴  B’s income = 6x = 6 × 500
    = ₹ 3000

    Correct Option: A

    A : B = 3 : 2 = 9 : 6
    B : C = 3 : 2 = 6 : 4
    ∴  A : B : C = 9 : 6 : 4

    ∴ 
    9x
    4x
    = 1000
    34

    ⇒  3x – x = 1000
    ⇒  2x = 1000
    ⇒  x = 500
    ∴  B’s income = 6x = 6 × 500
    = ₹ 3000



  1. Monthly income of A and B are in the ratio of 4 : 3 and their expenses bear the ratio 3 : 2. Each of them saves ₹ 6,000 at the end of the month, then the monthly income of A is









  1. View Hint View Answer Discuss in Forum

    Let the monthly income of A and B be ₹ 4x and ₹ 3x respectively and their expenditures be ₹ 3y and Rs. 2y respectively.
    ∴  4x – 3y = 6000
    and 3x – 2y = 6000
    ⇒  4x – 3y = 3x – 2y
    ⇒  x = y
    ∴  4x – 3y = 6000
    ⇒  x = 6000
    ⇒  A’s monthly income = 4x
    = ₹ 24000

    Correct Option: B

    Let the monthly income of A and B be ₹ 4x and ₹ 3x respectively and their expenditures be ₹ 3y and Rs. 2y respectively.
    ∴  4x – 3y = 6000
    and 3x – 2y = 6000
    ⇒  4x – 3y = 3x – 2y
    ⇒  x = y
    ∴  4x – 3y = 6000
    ⇒  x = 6000
    ⇒  A’s monthly income = 4x
    = ₹ 24000


  1. The ratio of the income to the expenditure of a family is 10 : 7. If the family’s expenses are ₹ 10,500, then savings of the family is









  1. View Hint View Answer Discuss in Forum

    Income of the family

    =
    10
    × 10500 = ₹ 15000
    7

    Savings = 15000 – 10500
    = ₹ 4500

    Correct Option: A

    Income of the family

    =
    10
    × 10500 = ₹ 15000
    7

    Savings = 15000 – 10500
    = ₹ 4500



  1. The ratio of income and expenditure of a person is 11 : 10. If he saves ₹ 9,000 per annum, his monthly income is









  1. View Hint View Answer Discuss in Forum

    Let the income of man be ₹ = 11x and his expenditure be ₹ 10x
    ∴  Savings = x = ₹ 9000
    ∴  Monthly income of man

    =
    11 × 9000
    = ₹ 8250
    12

    Correct Option: D

    Let the income of man be ₹ = 11x and his expenditure be ₹ 10x
    ∴  Savings = x = ₹ 9000
    ∴  Monthly income of man

    =
    11 × 9000
    = ₹ 8250
    12