Q. 124.3( 21 Votes )
A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.
Let the two - digit number be xy (i.e. 10x + y).
After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).
According to question -
(10x + y) = 7(x + y)
⇒ 3x = 6y
⇒ x = 2y.....(1)
(10x + y) - 27 = (10y + x)
⇒ 9x - 9y = 27
⇒ x - y = 3.....(2)
Substituting equation (1) into (2), we get -
y = 3
Substitute the value of y in equation (1), we get -
x = 6
Thus, the required number is 63.
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