Question

If a two digit number the ten's digit is there times the unit digit. When the number is decreased by 54 the digits are reversed. Find the number

Answer 1

• Let one's digit be M

and ten's digit be N.

• Original number = 10 × N + M

=> 10N + M

• Reverend number = 10M + N.

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☞ If a two digit number the ten's digit is three* times the unit digit.

=> N = 3M ________ (eq 1)

☞ When digits are reversed the number is decreased by 54.

=> 10N + M - 54 = 10M + N

=> 10N - N + M - 10M = 54

=> 9N - 9M = 54

=> N - M = 6

=> (3M) - M = 6 _____ [From (eq 1)]

=> 2M = 6

=> M = 3

• Put value of M in (eq 1)

=> N = 3(3)

=> N = 9

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Original number = 10N + M

=> 10 × 9 + 3

=> 90 + 3

=> 93

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93 is the number.

____________ [ANSWER]