Question

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by recvering the digits is 18 find the number ​

Answer 1

Answer:

Step-by-step explanation:

$\bf\underline{Given:-}$

The sum of the digits of a two digit number is 8.

the difference between the number and that formed by recvering the digits is 18.

$\bf\underline{To \ Find:-}$

The Number

$\bf\underline{Solution:-}$

Let the digit at unit place be x.

And the tens place be y.

Number = 10y + x

Number reversed = 10y + x

According to the question,

⇒ x + y = 8  --------- ( 1 )

⇒ (10y + x) - (10x + y) = 18

⇒ 9 (y - x) = 18

⇒ y - x = 2 ------- ( 2 )

By solving (1) and (2) we get :-

x = 3

y = 5

The number = 10y + x

The number = 10 × 5 + 3

The number = 53.

Hence, the required number is 53.

Answer 2

Question :-

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18 find the number ?

Answer:-

→ The required number is 53 .

To Find :-

Find the required number.

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Step - by - step explanation :-

Let ,numbers are "a" and "b" ,

Let, number at unit place is "a" and number at tens place is "b" .

According to the question,

→ a + b = 8 ..........(1)

And

also ,

Number is " a+10b " ,

when reversing this number we get

" 10a + b " .

• Difference between them is 18

→ ( a + 10b) - ( 10a + b) = 18

→ a + 10b - 10a - b = 18

→ - 9a + 9b = 18

→ 9 ( - a + b ) = 18

→ - a + b = 18/9

→ - a + b = 2 .........(2)

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Now , adding the eq.(1) and eq.(2),

→ a + b - a + b = 8+2

→ 2b = 10

→ b = 5

Now put b = 5 in eq ( 2) ,

→ - a + 5 = 2

→ - a = -3

→ a = 3

Then required number is ,

→ 10b+ a

Substitute the above values of "a" and "b",

→ 10× 5 + 3

→ 50+3

→ 53

Therefore the required number is 53.

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