Maths

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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