Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?​

Answer 1

Answer:

Step-by-step explanation:

Let the two digits of the number be x and y.

x + y = 9 … (1)

(10x + y) - (10y + x) = 27, or

9x - 9y = 27, or

x - y = 3  … (2)

Add (1) and (2)

2x = 12, or x = 3, so y = 9–6 = 3.

So the original number is 36

which on reversing becomes 63 and 63–36 = 27.

Correct.

Hence, the two-digit number required is evidently 36.

Answer 2

$\large\underline{ \underline{ \sf \: Solution : \: \: \: }}$

Let ,

the digits be x and y

Then , $\sf x + y = 9 \: ---- \: eq (i)$

the original number is 10x + y

On reversing , we get the new number as 10y + x

The new number is greater than the old number by 27 i.e

$\to \sf (10y + x) - (10x + y) = 27 \\ \\ \to \sf</p><p>9y - 9x = 27 \\ \\ \to \sf</p><p>y - x = 3 \: ---- \: eq (ii)$

Add eq (i) and eq (ii)

$\to \sf (x + y) + (y - x) = 9 + 3 \\ \\ \to \sf</p><p>2y = 12 \\ \\ \to \sf</p><p>y = 6$

Put the value of y = 6 in eq (i)

$\to \sf x + 6 = 9 \\ \\ \to \sf </p><p>x = 3$

Therefore , the original number is 36