Question

One says, “Give me a hundred, friend! I shall then become twice as rich as you.” The other replies, “If you give me ten, I shall be six times as rich as you.” Tell me what is the amount of their respective capital?

Answer 1

Let the money with the first person and the second person be Rs x and Rs y respectively.
According to the question

x + 100 = 2(y - 100)

x + 100 = 2y - 200

x - 2y = -300 .....(1)

6(x - 10) = (y + 10)

6x - 30 = y + 10

6x - y = 70 ......(2)

Multiplying equation (2) by 2, we obtain

12x - 2y = 140 .....(3)

Subtracting equation (1) from equation (3), we obtain:

12x - 2y - (x - 2y) = 140 -(-300)

12x - 2y - x + 2y = 140 + 300

11x = 140 + 300

11x = 440

x = `440/11`

x = 40

Putting the value of x in equation (1), we obtain

40 - 2y = -300

40 + 300 = 2y

2y = 340

y = 170

Thus, the two friends had  Rs 40 and Rs 170 with them.