Question

The sum of the digits of a certain two-digit number is 7. reversing its digits increases the number by 9. what is the number?

Answer 1

Let the tens digit of required no be X
And the unit digit be Y.
Required no. =10x+y
No, obtained on reversing
=10Y+x
Acoordibg to question.
X+y=7-----------{1}
10Y+X-10X+Y=9
Y-x=1 -------(2)
Now adding 1 and 2
X+Y=7
Y-X=1
2Y=8
Y=4
Now, putting on 1) equestion
X=3.
Then no will be
10*3+4.
34 ans

Answer 2

Answer:

The number is  34

Step-by-step explanation:

Let,

The units digit = x

The tens digit = 7 - x

Orignal Number :

⇒ 10 (7 - x) + x

⇒ 70 - 10x + x

⇒ 70 - 9x

★ Digit of the number reversing :

⇒ 10x + (7 - x)

⇒ 10x - x + 7

⇒ 9x + 7

★ According to the question:

The number with reversed digits increases

The original number by 9 :

So,

⇒ (70 - 9x) + 9 = (9x + 7)

⇒ 70 + 9 - 9x = 9x + 7

⇒ 79 - 9x = 9x + 7

⇒ 79 - 7 = 9x + 9x

⇒ 72 = 18x

⇒ 18x = 72

⇒ x = 72 / 18

⇒ x = 4

The unit digit = 4

The tens digit = 7 - x

⇒ 7 - 4

⇒ 3

The tens digit = 3

Therefore,

The number is  34