Question

the ratio between a two digit number and the number obtained on Reversing its digits is 4:7 . If the difference between the digits of Number is 3 , find the Number.

Answer 1

let the two digit's number be 10A+B,

then according to the question, we have

(10A+B)/(10B+A) = 4/7,

70A+7B=40B+4A,

then

70A-4A+7B-40B=0,

66A-33B=0,

2A-B=0,..............eq(1),

also it's given that

A-B=3,...........eq(2),

on solving these two equations we get

A=-3,
B=-6
igonre negetive sign here, we have

A=3,

B=6,

therefore

two digit number=10×3+6=36

Answer 2

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