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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-04-APP-01
Real-Life Applications — Assignment
Chapter: Linear Equations in Two Variables
Topic: Real-Life Applications
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Word problems are modelled by:
  • A.inequalities
  • B.linear equations
  • C.graphs
  • D.ratios
2.
"The sum of two numbers is $12$" is:
  • A.$x-y=12$
  • B.$x+y=12$
  • C.$xy=12$
  • D.$\tfrac{x}{y}=12$
3.
The cost of $x$ pens at $\textsf{Rs }5$ each is:
  • A.$5+x$
  • B.$5x$
  • C.$\tfrac{x}{5}$
  • D.$x-5$
4.
Two unknowns usually require:
  • A.one equation
  • B.two equations
  • C.no equation
  • D.three
5.
A linear cost relation graphs as a:
  • A.curve
  • B.straight line
  • C.circle
  • D.point
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write the cost of $x$ pens at $\textsf{Rs }5$ each.
7.
Write "the sum of two numbers is $12$" as an equation.
8.
If $3$ notebooks cost $\textsf{Rs }45$, find the cost $y$ of one.
9.
A taxi charges $\textsf{Rs }20$ plus $\textsf{Rs }10$ per km. Write the fare for $d$ km.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
The cost of $2$ kg apples and $1$ kg grapes is $\textsf{Rs }160$. Write the equation.
11.
A number is twice another; their sum is $18$. Write the two equations.
12.
The perimeter of a rectangle is $20$. Write the relation for length $l$ and breadth $b$.
13.
A two-digit number has tens digit $x$ and units digit $y$. Write its value.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A taxi charges $\textsf{Rs }20$ for the first km and $\textsf{Rs }12$ for each additional km. Write a linear equation for the fare $y$ over $x$ km and find the fare for $5$ km.
15.
The sum of two numbers is $30$, and one is $4$ more than twice the other. Form the two equations (do not solve).

Answer Key

Section A — Multiple Choice Questions
  1. (B) linear equations
  2. (B) $x+y=12$
  3. (B) $5x$
  4. (B) two equations
  5. (B) straight line
Section B — Short Answer (2 marks)
  1. $5x$.
  2. $x+y=12$.
  3. $\textsf{Rs }15$.
  4. $20+10d$.
Section C — Short Answer (3 marks)
  1. $2a+g=160$.
  2. $x=2y$ and $x+y=18$.
  3. $l+b=10$.
  4. $10x+y$.
Section D — Long Answer (5 marks)
  1. $y=12x+8$; fare for $5$ km $=\textsf{Rs }68$.
  2. $x+y=30$ and $x=2y+4$.
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