Question

One says, "give me 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

Those friends had Rs 40 and Rs 170 with them respectively.

Explanation :-

Let those friends were having Rs x and y with them.

Using the information given in the question, we obtain

x + 100 = 2(y − 100)

x + 100 = 2y − 200

x − 2y = −300 (i) And,

6(x − 10) = (y + 10)

6x − 60 = y + 10

6x − y = 70 (ii)

Multiplying equation (ii) by 2, we obtain

12x − 2y = 140 (iii)

Subtracting equation (i) from equation (iii), we obtain

11x = 140 + 300

11x = 440 x = 40

Using this in equation (i), we obtain

40 − 2y = −300

40 + 300 = 2y

2y = 340

y = 170

• Therefore, those friends had Rs 40 and Rs 170 with them respectively.

Answer 2

Answer:

Let those friends were having Rs x and y

with them.

Using the information given in the

question, we obtain

x + 100 = 2(y - 100)

epsilon + 100 = 2y - 200

x-2y = -300 (0) And

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

6x - 60 = y * 10

6x - y = 70(1)

Multiplying equation (0) by 2, we obtain

2x - 2y = 140.01

Subtracting equation () from equation (1),

we obtain

11x = 140 + 300

11x=440 x 40

Using this in equation), we obtain

10 - 2y = - 300

10 + 300 = 2y

2y = 340

r = 170

• Therefore, those friends hod Rs 40 and Rs 170 with them respectively.