Question

The ratio between a two-digit number obtained on reversing its digit is 4:7 if the difference between the digit of the number is 3 find the number

Answer 1

Let the ten's place digit be x and the unit's place digit be y.
Number = 10x + y
Reverse digit = 10y + x
A/Q,
10x + y / 10y + x = 4/7
7(10x + y) = 4(10y + x)
70x + 7y = 40y + 4x
70x - 4x + 7y - 40y = 0
66x - 33y = 0
33(2x - y) = 0
2x - y = 0 →(1)
x - y = 3 →(2)
subtracting eqn (1) from (2)
x - y - 2x + y = 3
-x = 3
x = -3
put x = -3 in eqn →(2)
y = -3 - 3
y = -6
No. = 10 x (3) + (6)
= 36