Find a two-digit number such that three times the tens digit is 2 less than twice the units digit and twice the number is 20 greater than the number obtained by reversing the digits
-
A.
24 -
B.
42 -
C.
74 -
D.
47 -
E.
72
Correct Answer: Option D
Explanation
Let the tens digits of the number be x and the unit digit be y
3x = 2y – 2
3x – 2y = -2…….(i)
If the digits are interchanged, the tens digit becomes y, the unit digit becomes x. Hence 2(10x + y) = 10y + x + 20
(20x + 2y) – (10y + x) = 20
19x – 8y = 20…..(ii)
Multiply eqn.(i) by 8 and eqn.(ii) by 2
24x – 16y = -16……(iii)
38x – 16y = 40……..(iv)
eqn(iv) – eqn(iii)
14x = 56
x = 4
Sub. for x = 4 in eqn(i)
3(4) – 2y = -2
14 = 2y
y = 7
So the original number is 10(4) + 7
i.e. 10x + y
= 47