Question

A number consists of two digits whose sum is 8 if 18 is added to the number its digits get interchanged the number is

Answer 1

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

• Original number = 10N + M

» The sum of the digits of a two digit number is 7.

→ M + N = 8

→ M = 8 - N ________ (eq 1)

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» If 18 is added to the number its digits get interchanged.

• Revered number = 10M + N

A.T.Q.

→ 10M + N = 10N + M + 18

→ 10M - M + N - 10N = 18

→ 9M - 9N = 18

→ M - N = 2

→ (8 - N) - N = 2 [From (eq 1)]

→ 8 - 2N = 2

→ - 2N = - 6

→ N = 3

Put value of N in (eq 1)

→ M = 8 - 3

→ M = 5

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Number = 10N + M => 10 × 5 + 3

→ 53

________ [ ANSWER ]

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