A number consists of two digits. The digits in the ten's place is 3 times the digit in the unit's place. If 54 is subtracted from the number the digits are reversed. The number is
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Let the digit at Tens place be x
The digit at unit place be y
The Number is 10x + y
ACCORDING TO THE QUESTION :-
x = 3y ... eq. 01
According to the second condition :
10x + y - 54 = 10y + x
=> 9x - 9y = 54
=> 9(x - y) = 9 × 6
=> x - y = 6 ... eq.02
Now we can solve the Equation 01 and 02 by substitution Method :-
x - y = 6
=> 3y - y = 6 [ from eq.01 , x = 3y ]
=> 2y = 6
=> y = 3
Now we can substitute the value of y in eq. 01 to get value of x
x = 3y
=> x = 3 × 3
=> x = 9
Hence the number is
Hence the number is 10x + y = 90 + 3 = 93 (ANS)
VERIFICATION
As given in the question if we subtract 54 from 93 the digits get reversed.
93 - 54 = 39
Hence our Answer is correct.
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