Question

10.) The sum of digits of a two digit number is 13. If the number formed by reversing
the digits is less than the original number by 27. Find the original number.​

Answer 1

Question:

The sum of the digits of a two digit number is 13. If the number formed by reversing the digits is less than the original number by 27 . Find the original number.

Answer:

The required number is 85 .

Solution:

Let the tens digit of the required number (original number) be x and its ones digit be y.

Then ,

The required number will be (10x+y).

Also,

The number formed by reversing the digits will be (10y+x).

It is given that;

The sum of the digits of the required number is 13.

Thus,

=> x + y = 13 --------(1)

Now,

According to the question,

The number formed by reversing the digits is less than the original number by 27.

Thus,

=> (10y + x) = (10x + y) - 27

=> 10x - x + y - 10y = 27

=> 9x - 9y = 27

=> 9(x - y) = 27

=> x - y = 27/9

=> x - y = 3 -------(2)

Now,

Adding eq-(1) and (2) ,we get;

=> x + y + x - y = 13 + 3

=> 2x = 16

=> x = 16/2

=> x = 8

Now,

Putting x = 8 in eq-(1) , we get ;

=> x + y = 13

=> 8 + y = 13

=> y = 13 - 8

=> y = 5

Hence,

The required number is;

85 .

Answer 2

Question :-

Given above ↑

Answer :-

→ Required number is 85.

Explanation :-

According to the question,

sum of digits of a two digit number is 13, ( a + b) = 13 ...eq.(1)

let "a" is at ten's place and "b" is at one's place ,

hence , → (10a + b)

also given that ,

when reversing the digits

it is = (10b +a)

and given that , it is less then original number by 27

→ (10b+ a) = (10a + b) -27

→ -9a +9b = -3

→ a - b = 3 ....eq.(2)

adding eq.(1) + eq.(2)

→ a + b + a - b = 13 +3

→ 2a = 16

→ a = 8

put a = 8 in eq.(1)

→ 8 + b = 13

→ b = 5

hence required number is -

→ 10a + b = 10×8 + 5

→ 85

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hope it will helps you.