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?
Linear Equations
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Question

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?

KnowledgeBoat · Accepted Answer

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 = = ₹ 40. Substituting value of x from equation (1), we get : ⇒ 2y - 40 = 300 ⇒ 2y = 300 + 40 ⇒ 2y = 340 ⇒ y = = ₹ 170. Hence, originally Rohit has ₹ 40 and Ajay has ₹ 170.

Mathematics

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?

Linear Equations

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