# 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. 👁
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. 👎

## Similar Questions

1. ### 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.

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

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

4. ### 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

1. ### Probability and statistics

What is the average of all possible five-digit numbers that can be formed by using each of the digits 8, 9, 1, 3 and 6 exactly once? Are you just supposed to try out all the possibilities and count them or is there like a formula

2. ### Mathematics:help me please anyone

The sum of the digits of a 3-digit number is three times the sum of the digits of a 2-digit number. When the 2-digit number is subtracted from the 3-digit number it gave another 2-digit number of which its first digit is three

3. ### 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

4. ### Math

A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?

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. ### finite

A 4-digit number is selected from the numbers {1,2,3,4,5,6} where the digits are selected without replacement. How many 4-digit numbers can be selected that are greater than 3000? How many even 4-digit numbers can be chosen? How

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 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