MathematicsA two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number.

A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number.


  1. A
    53
  2. B
    42
  3. C
    63
  4. D
    36 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given that a two-digit number is 4 times the sum of its digits and twice the product of the digits.
    Let x be the digit in the ones place and y be the digit in the tens place.
    So, the two-digit number = 10y + x.
    Since, given that number = 4 times sum of its digits, we get
    10y+x=4 x+y 10y+x=4x+4y 10y4y=4xx 6y=3x y= 3x 6 y= x 2 x=2y …………..(1)
    Also, given number = 2 times product of its digits,
    10y+x=2xy …………(2)
    Divide equation (2) by xy on both the sides.
    10y xy + x xy = 2xy xy 10 x + 1 y =2 ………….(3)
    Put x = 2y from equation (1) in equation (3).
    10 2y + 1 y =2 10 2y + 1 y × 2 2 =2 10 2y + 2 2y =2 10+2 2y =2 12 2y =2
    6 y =2 6 2 =y y=3
    Put y= 3 in equation (1).
    x=2 3 x=6
    Put x= 6 and y= 3 in equation 10y + x.
    Two-digit number is,
    =10×3+6 =30+6 =36 So, the two-digit number is 36.
    The correct option is (4).
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.