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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-03-APP-01
Applications in Daily Life — Assignment
Chapter: Pair of Linear Equations
Topic: Applications in Daily Life
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.
The sum of two numbers is $30$, difference $6$. The numbers are:
  • A.$20,10$
  • B.$18,12$
  • C.$15,15$
  • D.$24,6$
2.
Word problems are solved by forming:
  • A.graphs
  • B.linear equations
  • C.tables
  • D.ratios
3.
If $x+y=12$ and $x=2y$, then $y=$
  • A.$3$
  • B.$4$
  • C.$6$
  • D.$8$
4.
If $2$ pens and $3$ pencils cost $\textsf{Rs }18$, the equation is:
  • A.$2p+3q=18$
  • B.$3p+2q=18$
  • C.$p+q=18$
  • D.$5pq=18$
5.
A two-variable word problem usually needs:
  • A.$1$ equation
  • B.$2$ equations
  • C.$0$ equations
  • D.$3$ equations
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
The sum of two numbers is $25$ and difference $7$. Find them.
7.
$5$ books and $3$ pens cost $\textsf{Rs }70$; write the equation.
8.
A father is $3$ times as old as his son; their ages sum to $48$. Find the son's age.
9.
$2$ kg apples and $1$ kg grapes cost $\textsf{Rs }160$; write the equation.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
The larger of two numbers exceeds the smaller by $8$ and their sum is $50$. Find them.
11.
$2$ pencils and $3$ pens cost $\textsf{Rs }13$; $3$ pencils and $2$ pens cost $\textsf{Rs }12$. Find the cost of each.
12.
A number is $3$ times another and their sum is $48$. Find them.
13.
Two numbers are in the ratio $3:5$ and their sum is $64$. Find them.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A boat goes $30$ km upstream and $44$ km downstream in $10$ hours; and $40$ km upstream and $55$ km downstream in $13$ hours. Find the speed of the boat in still water and of the stream.
15.
The sum of a two-digit number and the number with digits reversed is $66$, and the digits differ by $2$. Find the number.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $18,12$
  2. (B) linear equations
  3. (B) $4$
  4. (A) $2p+3q=18$
  5. (B) $2$ equations
Section B — Short Answer (2 marks)
  1. $16$ and $9$.
  2. $5b+3p=70$.
  3. $12$ years.
  4. $2a+g=160$.
Section C — Short Answer (3 marks)
  1. $29$ and $21$.
  2. Pencil $\textsf{Rs }2$, pen $\textsf{Rs }3$.
  3. $36$ and $12$.
  4. $24$ and $40$.
Section D — Long Answer (5 marks)
  1. Boat $8$ km/h, stream $3$ km/h.
  2. $24$ or $42$.
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