Question

Rohit says to Ajay, “Give me hundred, I shall then become twice as rich as you.” Ajay replies, “if you give me ten, I shall be six times as rich as you.” How much does each have originally ?

Answer 1

Let Rohit has Rs. x and Ajay has Rs. y

When Ajay gives Rs. 100 to Rohit
x + 100 = 2(y - 100)
x - 2y = -300                        ...(1)

When Rohit gives Rs. 10 to Ajay
6(x-10) = y + 10
6x - y = 70                            ...(2)

Multiplying equation no. (2) By 2.
 12x - 2y = 140                     ...(3)

Subtracting equation (1) and (3)
    12x - 2y = 140
-      x - 2y = - 300   
     -     +      +          
     11x = 440
         x = 40

From (1)
40 - 2y = - 300
⇒ - 2y = - 340
⇒ y = 170
Thus, Rohit has Rs. 40 and Ajay has Rs. 170.