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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