Ratio, Proportion

Ratio, Proportion

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Aptitude miscellaneous
  1. The sum of three numbers is 116. The ratio of second to the third is 9 : 16 and the first to
    the third is 1 : 4. The second number is








  1. View Hint View Answer Discuss in Forum


    Therefore, second number

    =
    9
    		 × 116 =
    9
    		 × 116
    9 + 16 + 429

    = 36

    Correct Option: D


    Therefore, second number

    =
    9
    		 × 116 =
    9
    		 × 116
    9 + 16 + 429

    = 36

  1. Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is








  1. View Hint View Answer Discuss in Forum

    Let the numbers be 3x, 2x
    and 5x respectively.
    Now,  (3x)2 + (2x)2 + (5x)2
    = 1862
    ⇒  9x2 + 4x2 + 25x2 = 1862
    ⇒  38x2 = 1862

    ⇒  x2 =
    1862
    		 = 49
    38

    ⇒  x = √49 = 7
    ∴  The smallest number
    = 2x = 2 × 7 = 14

    Correct Option: C

    Let the numbers be 3x, 2x
    and 5x respectively.
    Now,  (3x)2 + (2x)2 + (5x)2
    = 1862
    ⇒  9x2 + 4x2 + 25x2 = 1862
    ⇒  38x2 = 1862

    ⇒  x2 =
    1862
    		 = 49
    38

    ⇒  x = √49 = 7
    ∴  The smallest number
    = 2x = 2 × 7 = 14

  1. The product of two positive integers is 1575 and their ratio is 9 : 7. The smaller integer is








  1. View Hint View Answer Discuss in Forum

    Let the integers be 9x and 7x respectively.
    According to the question,
    9x × 7x = 1575

    ⇒  x2 =
    1575
    63

    ⇒  x2 = 25
    ⇒  x = 5
    [x being positive (+ve) integer]
    ∴  Smaller integer
    = 7x = 7 × 5 = 35

    Correct Option: B

    Let the integers be 9x and 7x respectively.
    According to the question,
    9x × 7x = 1575

    ⇒  x2 =
    1575
    63

    ⇒  x2 = 25
    ⇒  x = 5
    [x being positive (+ve) integer]
    ∴  Smaller integer
    = 7x = 7 × 5 = 35

  1. The ratio of two numbers is 10 : 7 and their difference is 105. The sum of these numbers is








  1. View Hint View Answer Discuss in Forum

    Let the nos. be 10x & 7 x
    then, 10 x – 7x = 105
    ⇒  3x = 105 ⇒ x = 35
    ∴  Sum = 10x + 7x = 17x
    = 17 × 35 = 595

    Correct Option: A

    Let the nos. be 10x & 7 x
    then, 10 x – 7x = 105
    ⇒  3x = 105 ⇒ x = 35
    ∴  Sum = 10x + 7x = 17x
    = 17 × 35 = 595

  1. The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :








  1. View Hint View Answer Discuss in Forum

    Let the two numbers be x and y.
    ∴  According to question,
    x + y = 40     .....(i)
    x – y = 4     ....(ii)
    From equation (i) and (ii), we get
    x = 22 and y = 18
    ∴  Required ratio

    =
    22
    		 =
    11
    189

    = 11 : 9

    Correct Option: C

    Let the two numbers be x and y.
    ∴  According to question,
    x + y = 40     .....(i)
    x – y = 4     ....(ii)
    From equation (i) and (ii), we get
    x = 22 and y = 18
    ∴  Required ratio

    =
    22
    		 =
    11
    189

    = 11 : 9