# Maths

posted by .

The sum of the 2digits of a 2 digit number is 15. If th number formed by reversing the digits is less than the orginal number by 27.Find the orginal number

• Maths -

Let the number be ab

a+b=15
10b+a = 10a+b - 27

a + b = 15
-9a + 9b = -27

a + b = 15
a - b = 3

2a = 18
a=9
b=6

check: 69 = 96 - 27

• Maths -

Answering by logic and mental calculations:

Since the order of digits is not important (they will be reversed anyway), the only two-digit combinations that add up to 15 are (8,7) and (6,9).
(8,7) does not work because 87-78=9. Now try 96-69=27, which is obviously the answer.

• Maths -

When we have a two digit number, it can be expressed as :

10 a + b

In this case :

10 a + b = orginal number

The sum of the 2 digits is 15

a + b = 15 Subtract a to both sides

a - a + b = 15 - a

b = 15 - a

If you reverse the digits of 10 a + b, it will be :

10 b + a

10 b + a = orginal number - 27 Add 27 to both sides

10 b + a + 27 = orginal number - 27 + 27

10 b + a + 27 = orginal number

10( 15 - a ) + a + 27 = orginal number

150 - 10 a + a + 27 = orginal number

177 - 9 a = orginal number

Also

10 a + b = orginal number

10 a + 15 - a = orginal number

9 a + 15 = orginal number

177 - 9 a = 9 a + 15 Subtract 15 to both sides

177 - 9 a - 15 = 9 a + 15 - 15

162 - 9 a = 9 a Add 9 a to both sides

162 - 9 a + 9 a = 9 a + 9 a

162 = 18 a Divide both sides by 18

162 / 18 = a

9 = a

a = 9

b = 15 - a

b = 15 - 9 = 6

orginal number = 10 a + b = 10 * 9 + 6 = 90 + 6 = 96

## Similar Questions

These are extra credit questions, and I just want to know how to solve them. 1) The sum of two-digits of a two digit number is 14. If the number represented by reversing the digits is subtracted from the original number, the result …
2. ### algebra

A number consists of two digits. The sum of twice the tens digit an 5 times the units digit is 19. If the digits are reversed, the new number is 54 less than the original number. Find the number
3. ### Maths

The digits of a three digit number are in AP&their sum is 15.The number obtained by reversing the digits is 594 less than the original number.Find the number?
4. ### maths

Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has …
5. ### maths

the difference b/w a 3 digit number and the number formed by reversing its digits is 396,the difference of hundreds and the units digit,is one less than the sum of the units and tens digit .find the number
6. ### Math - Algebra

What is the linear equation that will represent the second statement in the following problem: "The sum of the digits of a three-digit number is 12. If the hundreds digit is replaced by the tens digit, the tens digit by the units digit, …
7. ### maths

The sum of digits of a 2 digit number is 7, If digits are interchanged the new number formed is 3 less than four times of original number. ( use 2 variables)
8. ### Math

The sum of the digits of a two-digit number is 14. The number formed by reversing the digits is 36 more than the original number. What is the original number?
9. ### maths

the ones digit of 2-digit number is twice the tens digit when the number formed by reversing the digit is added to the original number . The sum is 99 . find the original ?
10. ### maths

the digit at the tens place of a two digit number is four times that in the units place if the digits are reversed he new number will be 54 less than the orginal number. find the orginal number

More Similar Questions