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# 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? [From the Bijaganita of Bhaskara II]

[Hint: x + 100 = 2 (y -100), y + 10 = 6 (x -10)]

**Solution:**

We will be using the concept of two-variable linear equations to solve the given question.

Let the first friend have ₹ x

And the second friend has ₹ y

Using the information given in the question,

**Condition 1:** When second friend gives ₹ 100 to first friend;

x + 100 = 2 (y - 100)

x + 100 = 2y - 200

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

**Condition 2:** When first friend gives ₹ 10 to second friend;

y + 10 = 6 (x -10)

y + 10 = 6x - 60

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)

11x = 440

x = 440/11

x = 40

Substituting x = 40 in equation (1), we obtain

40 - 2y = - 300

2y = 40 + 300

y = 340/2

y = 170

Therefore, the first friend has ₹ 40, and the second friend has ₹ 170 with them.

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 3

**Video Solution:**

## 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?

Class 10 Maths NCERT Solutions Chapter 3 Exercise 3.7 Question 2

**Summary:**

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”. The first friend has ₹ 40, and the second friend has ₹ 170 with them.

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