Ratio, Proportion

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Aptitude miscellaneous
  1. Two number are in the ratio of 2 : 3. If 9 is added to each number, they will be in the ratio 3 : 4. What is the product of the two numbers ?








  1. View Hint View Answer Discuss in Forum

    Let the number be M and N
    According to the question.
    M/N = 2/3
    ⇒ 3M = 2N
    ⇒ 3M - 2N = 0 ...(i)

    And (M + 9)/(N + 9) = 3/4
    ⇒ 4M + 36 = 3N + 27
    ⇒ 4M - 3N = -9 ...(ii)

    Correct Option: C

    Let the number be M and N
    According to the question.
    M/N = 2/3
    ⇒ 3M = 2N
    ⇒ 3M - 2N = 0 ...(i)

    And (M + 9)/(N + 9) = 3/4
    ⇒ 4M + 36 = 3N + 27
    ⇒ 4M - 3N = -9 ...(ii)

    Multiplying Ex. (i) by 4 and Eq. (ii) by 3 and subtracting, we get N = 27
    Now, putting N = 27 in Eq. (i), we get 3M = 54
    ⇒ M = 18
    ∴ Product of the given numbers = 27 x 18 = 486

  1. Weekly income of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves ₹ 300 per week, then the weekly income of the first person is ?








  1. View Hint View Answer Discuss in Forum

    Let the income of two persons are 7k and 3k
    Expenditure of first person = 7k - 300
    Expenditure of second person = 3k - 300
    According to the question,
    (7k - 300)/(3k - 300) = 5/2

    Correct Option: C

    Let the income of two persons are 7k and 3k
    Expenditure of first person = 7k - 300
    Expenditure of second person = 3k - 300
    According to the question,
    (7k - 300)/(3k - 300) = 5/2
    ⇒ 14k - 600 = 15k - 1500
    ∴ k = 900
    Income of first person = 7k = 7 x 900
    = ₹ 6300

  1. Amit and Sudesh have invested in the ratio of 4 : 7. If both invested a total amount of ₹ 49500, then find the investment of Sudesh?








  1. View Hint View Answer Discuss in Forum

    Given total amount = ₹ 49500
    Let part of Amit's investment = 4k
    and part of sudesh's investment = 7k
    According to the question
    4k + 7k = 49500

    Correct Option: A

    Given total amount = ₹ 49500
    Let part of Amit's investment = 4k
    and part of sudesh's investment = 7k
    According to the question
    4k + 7k = 49500
    ⇒ 11k = 49500
    ⇒ k = 49500/11
    ∴ k = 4500
    Hence investment of sudesh = 7k = 7 x 4500 = 31500

  1. A bag contains ₹ 1, 50 paise and 25 paise coins in the ratio of 8 : 9 : 11. If the total money in the bag is ₹ 366, then find the number of 25 paise coins ?








  1. View Hint View Answer Discuss in Forum

    Let number of ₹ 1 coins = 8k
    Number of 50 paise coins = 9k
    Number of 25 paise coins = 11k

    According to the question,
    8k + 9k/2 + 11k/4 = 366

    Correct Option: A

    Let number of ₹ 1 coins = 8k
    Number of 50 paise coins = 9k
    Number of 25 paise coins = 11k

    According to the question,
    8k + 9k/2 + 11k/4 = 366
    ⇒ 32k + 18k + 11k = 1464
    ⇒ 61k = 1464
    ∴ k = 1464/61 = 24
    ∴ Number of 25 paise coins = 11k = 11 x 24 = 264

  1. If sum of ₹ 1664 is divided between P and Q in the ratio of 1/3 : 1/5, then find P's share ?








  1. View Hint View Answer Discuss in Forum

    Given that P's share : Q 's share = 1/3 : 1/5 = 5 : 3
    Here, a = 5, b = 3, N = 1664
    P's share = a/(a + b) x N

    Correct Option: D

    Given that P's share : Q 's share = 1/3 : 1/5 = 5 : 3
    Here, a = 5, b = 3, N = 1664
    P's share = a/(a + b) x N
    ∴ = 5/(5 + 3) x 1664 = (5/8) x 1664 = ₹ 1040