Question

the sum of the digit of two digit number is 7. If we add 45 to the number ,the digit are interchanged find the number

Answer 1

Answer:

The number is 16

Step-by-step explanation:

Let,

The units digit = x

The tens digit = 7 - x

Number :

⇒ 10x (7 - x) + x

⇒ 70 - 10x + x

⇒70 - 9x

If 45 is added

⇒ 70 + 45 - 9x

⇒ 115 - 9x

Digit of the number interchange:

⇒ 10x + (7 - x)

⇒10x - x + 7

⇒ 9x + 7

So,

⇒ 115 - 9x = 9x + 7

⇒ - 9x - 9x = 7 - 115

⇒ - 18x = - 108

⇒ 18x = 108

⇒ x = 108 / 18

⇒ x = 6

The units digit = 6

The tens digit = 7 - x

⇒ 7 - 6

⇒ 1

The tens digit = 1

Therefore,

The number is 16

Answer 2

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Lets the ones place digit and tens place digit X and y .

Number formed - 10x + y

After interchanging - 10y+x

According to question ,

10x+y+45 = 10y+x

9y -9x = 45

y-x = 5 .

Now add , x+y = 7and y-x = 5 .

y = 6 and X= 1.

Now the number will be 16 .