Question

The sum of the digits of a 2 digit no.is 8.The number obtained by interchange the digits exceed the given number by 18.find the given numbers

Answer 1

Answer:

The given number is 35

Step-by-step explanation:

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

Therefore , the number is

$10x + y$

The sum of the digits is given to be 8

$x + y = 8 - - (1)$

Again , The number obtained by interchange of the digits exceed the given number by 18

$10y + x = 10x + y + 18 \\ \implies10y - y = 10x - x + 18 \\ \implies9y = 9x + 18 \\ \implies9y = 9(x + 2) \\ \implies \: y = x + 2 - - - (2)$

Now ,

From equation (1) we have

$x + y = 8 \\ \implies \: x + x + 2 = 8 \\ \implies2x = 6 \\ \implies \: x = 3$

And from (2) we have

$y = x + 2 \\ \implies \: y = 3 + 2 \\ \implies \: y = 5$

Therefore , the number is

$10 \times 3 + 5 \\ = 30 + 5 \\ = 35$

Answer 2

• Let ten's digit be M and one's digit be N.

• Original number = 10M + N

» The sum of the digits of a 2 digit nunber is 8.

A.T.Q.

→ M + N = 8

→ N = 8 - M ________ (eq 1)

» The number obtained by interchange the digits exceed the given number by 18.

• Interchanged number = 10N + M

A.T.Q

→ 10N + M = 10M + N + 18

→ 10N - N + M - 10M = 18

→ 9N - 9M = 18

→ N - M = 2

→ 8 - M - M = 2

→ 8 - 2M = 2

→ - 2M = - 6

→ M = 3

Put value of M in (eq 1)

→ N = 8 - 3

→ N = 5

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We have to find the original number.

From above calculations we have M = 3 and N = 5

Also, we have original number = 10M + N

Put value of M and N in it

→ 10(3) + 5

→ 30 + 5

→ 35

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35

is the original number.

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