Q. 315.0( 1 Vote )


A two-digit number is 4 more than 6 times the sum of its digits. If 18 issubtracted from the number, the digits are reversed. Find the number.

Answer :


Let the units digit be x. Then the tens digit is y.
The number is 10x + y.
Condition I:
10x + y = 6(x + y) + 4
10x + y = 6x + 6y + 4
4x – 5y = 4 … (i)
Condition II:
10x + y – 18 = 10y + x
9x - 9y = 18
x - y = 2… (ii)
(i) 4x 5y = 4 (-)
(ii)
× 5 5x -  5y = 10
-x         = -6
x = 6
Substitute x = 6 in (i)
4(6)
5y = 4
24 5y = 4
-5y = 4 24
-5y = - 20
y = 4
Therefore the required number is 10(6) + 4 = 60 + 4 = 64.

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