Ratio, Proportion


  1. The number to be added to each of the numbers 7, 16, 43, 79 to make the numbers in proportion is









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    From the given options number = 5, because

    7 + 5
    =
    43 + 5
    16 + 579 + 5

    ⇒ 
    12
    =
    48
    2184

    [check other options likewise]
    Second Method :
    Here, a = 7, b=16, c = 43, d= 79
    Required number x =
    bc − ad
    (a + d) − (b + c)

    =
    16 × 43 − 7 × 79
    (7 + 79) − (16 + 43)

    =
    688 − 553
    86 − 79

    =
    35
    = 5
    7

    Correct Option: C

    From the given options number = 5, because

    7 + 5
    =
    43 + 5
    16 + 579 + 5

    ⇒ 
    12
    =
    48
    2184

    [check other options likewise]
    Second Method :
    Here, a = 7, b=16, c = 43, d= 79
    Required number x =
    bc − ad
    (a + d) − (b + c)

    =
    16 × 43 − 7 × 79
    (7 + 79) − (16 + 43)

    =
    688 − 553
    86 − 79

    =
    35
    = 5
    7


  1. Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, then the numbers are









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    Numbers = 2x, 3x and 4x
    ∴  (2x)2 + (3x)2 + (4x)2 = 1856
    ⇒  4x2 + 9x2 +16x2 = 1856
    ⇒  29x2 = 1856
    ⇒  x2 = 1856 ÷ 29 = 64
    ∴  x = √64 = 8
    ∴  Numbers = 16, 24 and 32

    Correct Option: B

    Numbers = 2x, 3x and 4x
    ∴  (2x)2 + (3x)2 + (4x)2 = 1856
    ⇒  4x2 + 9x2 +16x2 = 1856
    ⇒  29x2 = 1856
    ⇒  x2 = 1856 ÷ 29 = 64
    ∴  x = √64 = 8
    ∴  Numbers = 16, 24 and 32



  1. If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is :









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    (x + y)2 = 4xy
    ⇒  x2 + y2 + 2xy – 4xy = 0
    ⇒  (x – y)2 = 0 ⇒ x = y
    ⇒  x : y = 1 : 1

    Correct Option: C

    (x + y)2 = 4xy
    ⇒  x2 + y2 + 2xy – 4xy = 0
    ⇒  (x – y)2 = 0 ⇒ x = y
    ⇒  x : y = 1 : 1


  1. The ratio of number of balls in bags x,y is 2 : 3. Five balls are taken from bag y and are dropped in bag x. Number of balls are equal in each bag now. Number of balls in each bag now is









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    Number of balls in bag x and y respectively = 2a and 3a
    ∴  3a – 5 = 2a + 3
    ⇒  a = 5 + 3 = 8
    ∴  Total number of balls
    = 5a = 40
    ∴  Balls in each bag = 20

    Correct Option: B

    Number of balls in bag x and y respectively = 2a and 3a
    ∴  3a – 5 = 2a + 3
    ⇒  a = 5 + 3 = 8
    ∴  Total number of balls
    = 5a = 40
    ∴  Balls in each bag = 20



  1. The ratio between a two – digit number and the sum of the digits of that number is 4 : 1. If the digit at the unit’s place is 3 more than the digit at the ten's place, then the number is









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    Check through options
    Number = 36
    3 + 6 = 9; 6 – 3 = 3
    and 36 : 9 = 4 : 1
    Otherwise– 10x + y : x + y = 4 : 1
    ⇒  10x + (x + 3) : x + (x + 3) = 4 : 1

    ⇒ 
    11x + 3
    =
    4
    2x + 31

    ⇒  11x + 3 = 8x + 12
    ⇒  3x = 9 ⇒ x = 3 and y = 6
    Then the number is 36.

    Correct Option: C

    Check through options
    Number = 36
    3 + 6 = 9; 6 – 3 = 3
    and 36 : 9 = 4 : 1
    Otherwise– 10x + y : x + y = 4 : 1
    ⇒  10x + (x + 3) : x + (x + 3) = 4 : 1

    ⇒ 
    11x + 3
    =
    4
    2x + 31

    ⇒  11x + 3 = 8x + 12
    ⇒  3x = 9 ⇒ x = 3 and y = 6
    Then the number is 36.