Question

the difference between two number is 60. the ratio of the two number is 3:7. find the number

Answer 1

Based on the question  there can be two conditions,
CASE 1:- When x>y
x-y=60....(1)
y/x=3:7
7y=3x....(2)
Multiplying (1) by 7
7x-7y=420
From (2)
7x-3x=420
4x=420
x=105 
then, y=45
CASE 2:- When y>x
y-x=60 ....(1)
x/y=3:7
7x=3y...(2)
Multiplying (1) by 7
7y-7x=420
From 2,
4y=420

y=105 
so x=45 
Thus the numbers are (x,y)= (105,45) or (45,105)

Answer 2

Let the numbers to be a and b
           then,
                         a-b=60
                            a=60+b
             and,
                              a/b=3/7
               putting value of a = 60 + b from above equation
                             (60+b)/b = 3/7
               cross multiplication
                              420 + 7b = 3b
                                       420 = -4b
                                        b = -105
          put value of b in equation a = 60 + b
                                           a = 60 + (-105)
                                           a = -45
                 So the numbers are -105 and -45