the sum of the digits of a two-digit number is 10 if we reverse the digit the new number will be 54 more than the original number what is the original number
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Let xy be the required two-digit number.
Let x be the number which is in unit's digit.
Let y be the number which is in ten's digit.
Therefore the decimal expansion is 10x + y.
Given that if we reverse the digit the new number will be 54 more than the orginal number.
10y + x = 10x + y + 54
-9x + 9y = 54
-x + y = 6 ------- (1)
Given that sum of the digits of a two-digit number = 10.
x + y = 10 ------ (2).
On solving (1) & (2), we get
-x + y = 6
x + y = 10
--------------
2y = 16
y = 8.
Substitute y = 8 in (2), we get
x + y = 10
x + 2 = 10
x = 10 - 2
x = 8.
Therefore the original number = 28.
Hope this helps!
Let x be the number which is in unit's digit.
Let y be the number which is in ten's digit.
Therefore the decimal expansion is 10x + y.
Given that if we reverse the digit the new number will be 54 more than the orginal number.
10y + x = 10x + y + 54
-9x + 9y = 54
-x + y = 6 ------- (1)
Given that sum of the digits of a two-digit number = 10.
x + y = 10 ------ (2).
On solving (1) & (2), we get
-x + y = 6
x + y = 10
--------------
2y = 16
y = 8.
Substitute y = 8 in (2), we get
x + y = 10
x + 2 = 10
x = 10 - 2
x = 8.
Therefore the original number = 28.
Hope this helps!
Arya79:
Irs correct
Answered by
3
the answer is in attachment. and the no.( number) is 28
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