1. Questions

math

While adding ten two-digit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the original number is ten less than the number. What is the product of the digits of that number?

Please help how to obtain that number.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Suzanne

  1. let the 10th digit be interchanged and in form 10x+y
    therefore original sum
    => (a1+a2+...+a9) + 10x + y = S

    but the sum obtained was::: (a1+a2+...+a9) + 10y + x = S' bcoz the digits were interchanged

    "the sum of all the ten numbers increased by a value which was four less than that number"
    therefore!!
    S' - S = (10x+y) - 4
    the a1, a2...a9 gets cancelled out & what is left is
    => 9(y-x)=10x+y-4 => 8y-19x=(-4)-----------------------------...

    "three times the sum of digits of that original number is ten less than the number"
    therefore
    => 3(x+y) = 10x+y - 10 => 2y-7x = -10-------------------------------------...

    by (1) & (2), the y can be cancelled out by multiplying (2) with -4 & adding (1) & (2)

    the result we get is
    => 9x = 36 => x=4

    therefore by (2)
    2y -7.4= -10 => y=9

    therefore x.y = 36

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    vikas

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    what is the sum of the digits of the largest even 3 digit number which is not changed when its units and hundreds digit are interchanged

  2. maths

    can you replace the stars with figures **** x 3 ______ ***** the whole calculation uses each of the digits 0-9 once and once only the 4 figure number contains three consecutive numbers which are not in order. the third digit is

  3. College

    Three(3) digit numbers can be formed from the digits 0,1,3,5,7 and 8. How many numbers can be formed without repeats. (A) if the 3 digits numbers must be divisible by 5. (b) if the 3 digits number must be a multiple of 2

  4. math

    find how many six-digit numbers can be formed from the digits 2,3,4,5,6,7 (with repetitions) if a) numbers formed must be even b) the numbers formed must be divisble by 25 c) the odd digits must occupy even position (2nd, 4th,

  1. math

    While adding ten two-digit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the

  2. math problem

    My ID number is quite remarkable.Its a 9 digit number with the digits 1-9 appearing only once. The entire 9 digit nuymber is divisible by 9. If you remove the last digit, the remaining 8 digit number is divisible by 8. If you

  3. Maths

    In A Two Digit Number, The Sum Of The Digits Is 14. Twice The Tens Digit Exceeds The Units Digit By One.Find the Numbers.

  4. Math

    If no digit can be used more than once, how many 5-digit numbers can be formed only using the numbers 3,8,1,2,5, and 7? A: 350 numbers B: 717 numbers C: 722 numbers D: 720 numbers I guessed the answer 720 and got it right but I

  1. PROBLEM SOLVING IN MATHEMATICS

    there are two prime numbers between 100 and 199 such that the ten digits is a prime number, the ones digit is a prime number and the tens and ones digits taken together are a 2 digit prime number. find the sum of these 2 prime

  2. math

    Five three digit numbers including N were to be added. While adding, the reverse of N was added by mistake instead of N. Hence the summ increased by 11 times the summ of the digits of N.Eight times the difference of N's units and

  3. math

    three digit numbers are to be formed from digits 0,1,2,3...9 if repetitionis allowed. (a) how many of such numbers can be formed? (b)how manyof the numbers in(a)are divisible by 3 and how many of 9? (c) find the sum of all the

  4. balayan national highschool

    The hundred thousands digits of a six-digit even number is 3 more than the thousand digit, which is twice the ones digit. Give at least four numbers that satisfy the given condition.

View more similar questions or ask a new question.