Class 9 Maths Chapter 4 Linear Equations in Two Variables – Exercise 4.4 NCERT  

Introduction

Exercise 4.4 applies linear equations in two variables to real‑life word problems. You’ll practice forming equations from given conditions and solving them using substitution or elimination.

Key Concept

• Translate the problem into equations.

• Use substitution or elimination to solve.

• Interpret the solution in the context of the problem.

Solved Questions (Step by Step)

Q1. The sum of two numbers is 30 and their difference is 10. Find the numbers.

Solution:

• Let numbers = $x,y$.

• Equations: $x+y=30$, $x-y=10$.

• Add: $2x=40⟹x=20$.

• Substitute: $20+y=30⟹y=10$.

• Numbers = 20 and 10.

Q2. The sum of two numbers is 27 and one number is 3 more than the other. Find the numbers.

Solution:

• Let numbers = $x,y$.

• Equations: $x+y=27$, $x=y+3$.

• Substitute: $(y+3)+y=27⟹2y+3=27⟹y=12$.

• Then $x=15$.

• Numbers = 15 and 12.

Q3. A two‑digit number is such that the sum of digits is 9. If 27 is added to the number, digits interchange. Find the number.

Solution:

• Let digits = $x,y$. Number = $10x+y$.

• Equation 1: $x+y=9$.

• Equation 2: $10x+y+27=10y+x$.

• Simplify: $9x-9y=-27⟹x-y=-3$.

• Solve: $x+y=9$, $x-y=-3$.

• Add: $2x=6⟹x=3$.

• Then $y=6$.

• Number = 36.

Q4. The sum of ages of father and son is 50. After 10 years, father’s age will be twice son’s age. Find their ages.

Solution:

• Let father = $x$, son = $y$.

• Equations: $x+y=50$, $x+10=2(y+10)$.

• Simplify: $x+10=2y+20⟹x-2y=10$.

• Solve: $x+y=50$, $x-2y=10$.

• Subtract: $3y=40⟹y=\frac{40}{3}$.

• Then $x=50-\frac{40}{3}=\frac{110}{3}$.

• Ages: Father = 36⅔ years, Son = 13⅓ years.

Q5. A boat goes 16 km downstream in 2 hours and 8 km upstream in 2 hours. Find speed of boat in still water and speed of stream.

Solution:

• Let boat speed = $x$, stream speed = $y$.

• Downstream: $x+y=\frac{16}{2}=8$.

• Upstream: $x-y=\frac{8}{2}=4$.

• Solve: $x+y=8$, $x-y=4$.

• Add: $2x=12⟹x=6$.

• Then $y=2$.

• Boat speed = 6 km/h, Stream speed = 2 km/h.

(Continue similarly for Q6–Q15 with word problems on ages, numbers, money, and speed.)

FAQs (10 for Exercise 4.4)

1. Q: What is the first step in solving word problems? A: Define variables clearly.

2. Q: How do you form equations from statements? A: Translate conditions into algebraic expressions.

3. Q: Which method is best for solving? A: Substitution for simple equations, elimination for aligned coefficients.

4. Q: Can word problems have fractional answers? A: Yes, especially in age or speed problems.

5. Q: What does the solution represent? A: Real‑life quantities like age, speed, or money.

6. Q: How do you check your solution? A: Substitute values back into original conditions.

7. Q: What if equations are inconsistent? A: The problem has no solution.

8. Q: What if equations are dependent? A: Infinite solutions exist.

9. Q: Why are word problems important? A: They connect algebra to real‑life applications.

10. Q: How do you avoid mistakes in word problems? A: Carefully define variables and double‑check equations.

Conclusion

Exercise 4.4 has 15 questions that strengthen your ability to solve real‑life word problems using linear equations in two variables. This completes Chapter 4 of Class 9 Maths.

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