Question

If seven times a two digit number is four times the number obtained by reversing its digits . if the difference of the digits is 3 , find the numbers?

Answer 1

let the digits be x ,y
x-y=3 (i)

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 (ii)

evaluating eqn i & eqn ii we get,
x-y=3
2x-y=0
=> -x = 3 =>x = 3

putting value of x in eqn i we get,
x-y=3
=> 3-y =3
=> y= 3 +3 = 6

so 1st digit is 3 and 2nd digit is 6

Answer 2

Answer:

36

Step-by-step explanation:

Let the unit digit be a and tenth unit be b .

So , number = 10 b + a

It's said number is seven times is equal to reversing the order of its digit.

= > 7 ( 10 b + a ) = 4 ( 10 a + b )

= > 70 b + 7 a = 40 a + 4 b

= > 66 b = 33 a

= > a = 2 b ... ( i )

Also given numbers' difference is 3 .

a - b = 3  ( ii )

From ( i ) and ( ii ) we get :

a b - b = 3

b = 3

= > a = 6

Hence number = > 30 + 6

= > 36.