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.

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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