Question

The sum of digit of two digit no.is 15 .On reserving the order of digit , the new no. exceeds the original no. by 27 . Find the no.

Answer 1

Step-by-step explanation:

Given :-

The sum of digit of two digit no.is 15 .

On reserving the order of digit , the new no. exceeds the original no. by 27 .

To find :-

Find the number ?

Solution:-

Let the digit at ten's place be X

Then the place value of X = 10X

Let the digit at ones place be Y

Then the place value of Y = Y

Then the number = 10X+Y

If the digits are reversed then the new number = 10Y+X

Given that

The sum of digit of two digit number = 15

=> X+Y = 15

=>X = 15-Y ---------------(1)

And

On reserving the order of digit , the new number exceeds the original number by 27 .

=> New number = Original number+27

=> 10Y+X = 10X+Y +27

=>10Y+X-10X-Y = 27

=> (10Y-Y) +(X-10X) = 27

=> 9Y-9X = 27

=> 9(Y-X) = 27

=> Y-X = 27/9

=> Y-X = 3

=> Y-(15-Y) = 3 (from (1))

=> Y-15+Y = 3

=> 2Y-15 = 3

=>2Y = 3+15

=>2Y = 18

=>Y = 18/2

=> Y = 9------(2)

On Substituting the value of Y in (1) then

X = 15-9

=>X = 6

Therefore, X = 6 and Y = 9

Answer:-

The required number for the given problem is 69

Check:-

X = 6 and Y = 9

Sum of the digits = 6+9=15

The number = 69

The new number obtained by reversing the digits = 96

= 69+27

= 96

= Original number+27

Verified the given relations in the given problem.

Used Method:-

• Substitution method