Rohit says to Ajay, "Give me a 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?

Let Rohit have ₹ x and Ajay have ₹ y.

According to first part of question :

⇒ x + 100 = 2(y - 100)

⇒ x + 100 = 2y - 200

⇒ 2y - x = 100 + 200

⇒ 2y - x = 300 ………..(1)

According to second part of question :

⇒ y + 10 = 6(x - 10)

⇒ y + 10 = 6x - 60

⇒ y - 6x = -60 - 10

⇒ y - 6x = -70

Multiplying both sides of the above equation by 2, we get :

⇒ 2(y - 6x) = 2 × -70

⇒ 2y - 12x = -140 ………..(2)

Subtracting equation (2) from (1), we get :

⇒ 2y - x - (2y - 12x) = 300 - (-140)

⇒ 2y - x - 2y + 12x = 300 + 140

⇒ 11x = 440

⇒ x = $\dfrac{440}{11}$ = ₹ 40.

Substituting value of x from equation (1), we get :

⇒ 2y - 40 = 300

⇒ 2y = 300 + 40

⇒ 2y = 340

⇒ y = $\dfrac{340}{2}$ = ₹ 170.

Hence, originally Rohit has ₹ 40 and Ajay has ₹ 170.