A two digit number is 3 more than 4 times the sum of digits . If 18 is added to the number its digits are reversed . Find the number
Answers
• Let's one's digit be M and ten's digit be N.
Number = 10N + M
» A two digit number is 3 more than 4 times the sum of digits.
A.T.Q.
=> 10N + M = 4(M + N) + 3
=> 10N + M = 4M + 4N + 3
=> 10N - 4N + M - 4M = 3
=> 6N - 3M = 3
=> 2N - M = 1
=> - M = 1 - 2N
=> M = 2N - 1 _______ (eq 1)
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» If 18 is added to the number its digits are reversed.
Revered number = 10M + N
A.T.Q.
=> 10M + N = 10N + M + 18
=> 10M - M + N - 10N = 18
=> 9M - 9N = 18
=> M - N = 2
=> (2N - 1) - N = 2 [From (eq 1)]
=> 2N - N - 1 = 2
=> N = 3
Put value of N in (eq 1)
=> M = 2(3) - 1
=> M = 6 - 1
=> M = 5
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From above calculations we have M = 5 and N = 3.
Where.. M = one's digit and N = ten's digit.
Now put their values to get the number.
=> 10(3) + 5
=> 30 + 5
=> 35
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Number = 35
_________ [ ANSWER ]
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