the sum of the two digit number is 12. if the new no. formes by reversing the digit is greater than the originol no. by 54. find the originol no.
Answers
The Original Number is 39
Given :
Sum of the Digits = 12
The number with interchanged digits is greater than the original number by 54.
To Find :
The Number
Solution :
- Units place as x
- Tens place as 10(12 - x)
x + 10(12 - x)
x + 120 - 10x
-9x + 120 ......... [ Original Number ]
- Units Place = (12 - x)
- Tens Place = 10(x)
12 - x + 10x
12 + 9x .......... [ Number with Reversed Digits ]
The number with interchanged digits is greater than the original number by 54.
★
Units Place = 9
★ Value of 10(12 - x)
The Original Number -
The Original Number is 39.
Reversed digits of 39 = 93
Check if 93 is more 39 by 54 or not.
The Original Number is 39.
» The sum of the two digit number is 12.
• Let one's digit be M and ten's digit be N.
• Original number = 10N + M
A.T.Q.
→ M + N = 12
→ M = 12 - N _________ (eq 1)
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» The new number formes by reversing the digit is greater than the originol number by 54.
• Reversed number = 10M + N
A.T.Q.
→ 10M + N = 10N + M + 54
→ 10M - M + N - 10N = 54
→ 9M - 9N = 54
→ M - N = 6
→ (12 - N) - N = 6 [From (eq 1)]
→ 12 - N - N = 6
→ - 2N = 6 - 12
→ - 2N = - 6
→ N = 3
Put value of N in (eq 1)
→ M = 12 - 3
→ M = 9
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From above calculations we get M = 9 and N = 3
We have to find the number i.e 10N + M
Put value of N and M in it
→ 10(3) + 9
→ 30 + 9
→ 39
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39 is the original number.
_______ [ ANSWER ]
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✡ VERIFICATION :
From above calculations we get N = 3 and M = 9
Put them in this equation : 10M + N = 10N + M + 54
=> 9M - 9N = 54
=> 9(9) - 9(3) = 54
=> 81 - 27 = 54
=> 54 = 54
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