Number System


  1. The product of two positive numbers is 2500. If one number is four times the other, then the sum of the two numbers is :









  1. View Hint View Answer Discuss in Forum

    Let one of the positive numbers be x.
    ∴  The other will be 4x
    Now, 4x × x = 2500
    ⇒  x2 = 2500 ÷ 4 = 625
    ∴  x = 625 = 25
    ∴  Sum of the two numbers
    = 5x = 5 × 25 =125

    Correct Option: B

    Let one of the positive numbers be x.
    ∴  The other will be 4x
    Now, 4x × x = 2500
    ⇒  x2 = 2500 ÷ 4 = 625
    ∴  x = 625 = 25
    ∴  Sum of the two numbers
    = 5x = 5 × 25 =125


  1. 380 mangoes are distributed among some boys and girls who are 85 in number. Each boy gets four mangoes and each girl gets five. The number of boys is









  1. View Hint View Answer Discuss in Forum

    Let number of boys = x
    and number of girls = 85 – x
    According to the question,
    x × 4 + (85 – x ) × 5 = 380
    ⇒  4x + 425 – 5x = 380
    ⇒  x = 45

    Correct Option: D

    Let number of boys = x
    and number of girls = 85 – x
    According to the question,
    x × 4 + (85 – x ) × 5 = 380
    ⇒  4x + 425 – 5x = 380
    ⇒  x = 45



  1. 99
    1
    + 99
    2
    + 99
    3
    + 99
    4
    + 99
    5
    + 99
    6
    777777

    is equal to









  1. View Hint View Answer Discuss in Forum

    Expression = 99 +
    1
    + 99 +
    2
    + 99 +
    3
    + .......+ 99 +
    6
    7777

    = (99 ×6) +
    1
    +
    2
    +
    3
    +
    4
    +
    5
    +
    6
    777777

    = 594 +
    1 + 2 + 3 + 4 + 5 + 6
    7


    = 594 +
    21
    = 594 + 3 = 597
    7

    Correct Option: D

    Expression = 99 +
    1
    + 99 +
    2
    + 99 +
    3
    + .......+ 99 +
    6
    7777

    = (99 ×6) +
    1
    +
    2
    +
    3
    +
    4
    +
    5
    +
    6
    777777

    = 594 +
    1 + 2 + 3 + 4 + 5 + 6
    7


    = 594 +
    21
    = 594 + 3 = 597
    7


  1. The sum and product of two numbers are 10 and 24 respectively. The sum of their reciprocals is









  1. View Hint View Answer Discuss in Forum

    Let the numbers be x and y.
    ∴  x + y = 10 and xy = 24

    ∴ 
    x + y
    =
    1
    +
    1
    =
    10
    =
    5
    xyyx2412

    Correct Option: B

    Let the numbers be x and y.
    ∴  x + y = 10 and xy = 24

    ∴ 
    x + y
    =
    1
    +
    1
    =
    10
    =
    5
    xyyx2412



  1. The product of two numbers is 120. The sum of their squares is 289. The difference of these two numbers is









  1. View Hint View Answer Discuss in Forum

    Let the numbers be x and y.
    xy = 120
    x2 + y2 = 289
    (x − y)2 = x2 + y2 − 2xy
    = 289 – 2× 120 = 289 – 240 = 49
    ∴  x – y = 7

    Correct Option: B

    Let the numbers be x and y.
    xy = 120
    x2 + y2 = 289
    (x − y)2 = x2 + y2 − 2xy
    = 289 – 2× 120 = 289 – 240 = 49
    ∴  x – y = 7