Pair of Linear Equations in Two Variables — Question Ex 3.7 Q2
Back to all questionsEx 3.7 Class 10 Maths Question 2.
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?
Let the two friends have ₹ x and ₹ y.
According to the first condition:
One friend has an amount = ₹(x + 100)
Other has an amount = ₹ (y – 100
∴ (x + 100) =2 (y – 100)
⇒ x + 100 = 2y – 200
⇒ x – 2y = -300 …(i)
According to the second condition:
One friend has an amount = ₹(x – 10)
Other friend has an amount =₹ (y + 10)
∴ 6(x – 10) = y + 10
⇒ 6x – 60 = y + 10
⇒ 6x-y = 70 …(ii)
Multiplying (ii) equation by 2 and subtracting the result from equation (i), we get:
x – 12x = – 300 – 140
⇒ -11x = -440
⇒ x = 40
Substituting x = 40 in equation (ii), we get
6 x 40 – y = 70
⇒ -y = 70- 24
⇒ y = 170
Thus, the two friends have ₹ 40 and ₹ 170.
CBSE Class 10 Pair of Linear Equations — Complete Guide
This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.
Quick Revision: Key Concepts
- Unique solution: a1/a2 ≠ b1/b2 (intersecting lines)
- Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
- No solution: a1/a2 = b1/b2 ≠ c1/c2 (parallel lines)
- Methods: Substitution, Elimination, Cross-multiplication
- Reducible equations: Substitute u = 1/x, v = 1/y
Most Important Questions
- Determine consistency of a system of equations
- Solve using elimination or substitution method
- Word problems: age, speed, fraction, geometry type
- Equations reducible to linear form (1/x, 1/y type)
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