EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Equations and Simultaneous Linear Equations
Grade : ICSE Grade IX
License : Non Commercial Use
Question 1
1.
A motor boat can move at a speed of 10.16 m/sec in still water. If it goes downstream for 215.48 sec, it travels a distance of 4344.00 m. What is the speed of the stream?
  • (i)
    10.00 m/sec
  • (ii)
    11.00 m/sec
  • (iii)
    9.00 m/sec
  • (iv)
    12.00 m/sec
  • (v)
    8.00 m/sec
Question 2
2.
    • Which of the following equations is equivalent to
    • (
      x
      +
      8
      		)
      =
      0
  • (i)
    x
    =
    (
    −
    8
    		)
  • (ii)
    x
    =
    (
    −
    4
    		)
  • (iii)
    x
    =
    (
    −
    11
    		)
  • (iv)
    x
    =
    (
    −
    5
    		)
  • (v)
    x
    =
    (
    −
    12
    		)
Question 3
3.
    • Which of the following equations is the same as
    • (
      −
      x
      +
      7
      		)
      =
      (
      −
      3
      x
      −
      6
      		)
  • (i)
    (
    −
    x
    +
    5
    		)
    =
    (
    −
    3
    x
    −
    4
    		)
  • (ii)
    (
    −
    x
    +
    9
    		)
    =
    (
    −
    3
    x
    −
    3
    		)
  • (iii)
    (
    −
    x
    +
    9
    		)
    =
    (
    −
    3
    x
    −
    5
    		)
  • (iv)
    (
    −
    x
    +
    13
    		)
    =
    (
    −
    3
    x
    −
    4
    		)
  • (v)
    (
    −
    x
    +
    9
    		)
    =
    (
    −
    3
    x
    −
    4
    		)
Question 4
4.
    • Which of the displayed lines represent the equation
    • x
      =
      (
      −
      2
      		)
  • (i)
      • line with point
      • R
  • (ii)
      • line with point
      • S
  • (iii)
      • line with point
      • U
  • (iv)
      • line with point
      • Q
  • (v)
      • line with point
      • T
Question 5
5.
    • A and B together can do a piece of work in
    • 4
      2
      3
      days
    • .
    • They work together for
    • 2
      days
    • and then A leaves.
    • B completes the remaining work in
    • 8
      days
    • .
    • In how much time can each of them do the work seperately?
  • (i)
    (
    7
    days
    ,
    14
    days
    )
  • (ii)
    (
    6
    days
    ,
    14
    days
    )
  • (iii)
    (
    7
    days
    ,
    13
    days
    )
  • (iv)
    (
    7
    days
    ,
    15
    days
    )
  • (v)
    (
    8
    days
    ,
    14
    days
    )
Question 6
6.
    • Solve the following pair of equations :
    •   −  
       
       
      2
       
       
      √
      x
      		  −  
       
       
      5
       
       
      √
      y
      =
      -36
    •   −  
       
       
      4
       
       
      √
      x
      		  +  
       
       
      9
       
       
      √
      y
      =
      42
  • (i)
    (
    1
    9
    ,
    1
    36
    )
  • (ii)
    (
    1
    3
    ,
    1
    36
    )
  • (iii)
    (
    1
    9
    ,
    (
    -1
    36
    		 )
    )
  • (iv)
    (
    1
    9
    ,
    1
    34
    )
  • (v)
    (
    1
    11
    ,
    1
    36
    )
Question 7
7.
    • Which of the following equations is the same as
    • (
      4
      x
      +
      2
      		)
      =
      (
      −
      8
      x
      −
      3
      		)
  • (i)
    (
    8
    x
    −
    5
    		)
    =
    (
    −
    4
    x
    −
    10
    		)
  • (ii)
    (
    8
    x
    −
    5
    		)
    =
    (
    −
    12
    x
    +
    4
    		)
  • (iii)
    (
    3
    x
    +
    1
    		)
    =
    (
    −
    7
    x
    −
    2
    		)
  • (iv)
    9
    =
    (
    −
    4
    x
    −
    10
    		)
  • (v)
    (
    5
    x
    +
    3
    		)
    =
    (
    −
    9
    x
    −
    4
    		)
Question 8
8.
    • Find the set of points satisfying the equation
    • (
      6
      x
      +
      4
      y
      −
      3
      		)
      =
      0
  • (i)
    • (
      (
      −
      2
      )
      ,
      15
      4
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      9
      4
      )
    • ,
    • (
      0
      ,
      3
      4
      )
    • ,
    • (
      1
      ,
      (
      −
      3
      4
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      1
      4
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      15
      4
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      9
      4
      )
    • ,
    • (
      0
      ,
      3
      4
      )
    • ,
    • (
      1
      ,
      (
      −
      3
      4
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      4
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      15
      4
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      9
      4
      )
    • ,
    • (
      1
      ,
      (
      −
      1
      4
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      3
      4
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      4
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      15
      4
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      9
      4
      )
    • ,
    • (
      0
      ,
      3
      4
      )
    • ,
    • (
      0
      ,
      1
      4
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      4
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      15
      4
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      9
      4
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      5
      4
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      3
      4
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      4
      )
      )
Question 9
9.
    • Find the fourth proportional of
    • 30
    • ,
    • 5
    • and
    • 24
  • (i)
    24
  • (ii)
    2
  • (iii)
    6
  • (iv)
    5
  • (v)
    4
Question 10
10.
    • The point of intersection of x-axis and y-axis
  • (i)
    (
    1
    ,
    0
    )
  • (ii)
    (
    0
    ,
    9
    )
  • (iii)
    (
    0
    ,
    0
    )
  • (iv)
    (
    1
    ,
    1
    )
Question 11
11.
    • Which of the following equations is not the same as
    • (
      8
      x
      +
      2
      		)
      =
      0
  • (i)
    (
    −
    40
    x
    −
    10
    		)
    =
    0
  • (ii)
    (
    24
    x
    +
    6
    		)
    =
    0
  • (iii)
    (
    −
    24
    x
    −
    6
    		)
    =
    (
    −
    3
    		)
  • (iv)
    (
    16
    x
    +
    4
    		)
    =
    0
  • (v)
    (
    32
    x
    +
    8
    		)
    =
    0
Question 12
12.
    • In an examination, the ratio of passes to failures was 2 : 1.
    • Had 10 less appeared and 20 less passed, the ratio of passes to failures would have been 2 : 3.
    • How many students appeared for the examination?
  • (i)
    65
  • (ii)
    60
  • (iii)
    70
  • (iv)
    55
  • (v)
    50
Question 13
13.
The ages of A and B are in the ratio 9 : 8. 7 years hence, their ages will be in the ratio 10 : 9. Find their present ages.
  • (i)
    54
    		:
    48
  • (ii)
    81
    		:
    72
  • (iii)
    45
    		:
    40
  • (iv)
    63
    		:
    56
Question 14
14.
    • The additive inverse of the expression
    • x
    • is
  • (i)
    (
    −
    2
    x
    		)
  • (ii)
    (
    −
    x
    		)
  • (iii)
    x
  • (iv)
    (
    −
    3
    x
    		)
Question 15
15.
    • Solve
    •  
    • (
      y
      −
      3
      		)
      =
      0
      (
      y
      −
      6
      		)
      =
      0
  • (i)
    No solution
  • (ii)
    (
    1
    ,
    (
    −
    4
    )
    )
  • (iii)
    Infinite solutions
  • (iv)
    (
    4
    ,
    (
    −
    9
    )
    )
  • (v)
    (
    6
    ,
    (
    −
    7
    )
    )
Question 16
16.
Which of the following is a linear equation in two variable?
  • (i)
    (
    4
    x
    2
     
    +
    12
    x
    y
    −
    18
    x
    −
    16
    y
    2
     
    −
    32
    y
    +
    20
    		)
    =
    0
  • (ii)
    (
    −
    7
    x
    −
    y
    +
    8
    z
    −
    7
    		)
    =
    (
    5
    x
    −
    8
    y
    +
    6
    z
    +
    7
    		)
  • (iii)
    (
    9
    x
    +
    5
    		)
    =
    (
    −
    7
    x
    −
    6
    		)
  • (iv)
    (
    21
    x
    2
     
    −
    55
    x
    +
    36
    		)
    =
    (
    −
    5
    x
    +
    3
    		)
  • (v)
    (
    4
    x
    +
    4
    y
    +
    6
    		)
    =
    (
    −
    8
    x
    −
    2
    y
    −
    1
    		)
Question 17
17.
Two numbers are in the ratio 7 : 9. If 20 is added to each number, the ratio becomes 59 : 73. Find the numbers.
  • (i)
    98
    		:
    126
  • (ii)
    112
    		:
    144
  • (iii)
    105
    		:
    135
  • (iv)
    91
    		:
    117
  • (v)
    84
    		:
    108
Question 18
18.
    • Solve :
    •  
       
      (
      −
      3
      x
      +
      5
      		)
       
       
      6
      		  +  
       
       
      (
      −
      3
      x
      −
      5
      		)
       
       
      12
      =
       
       
      (
      3
      x
      −
      4
      		)
  • (i)
    11
    9
  • (ii)
    55
    47
  • (iii)
    51
    43
  • (iv)
    17
    15
  • (v)
    53
    45
Question 19
19.
    • Solve the following pair of equations :
    •  
       
      8
       
       
      (
      x
      +
      y
      		)
      		  +  
       
       
      1
       
       
      (
      x
      −
      y
      		)
      =
       
       
      (
      −
      18
      		)
    •   −  
       
       
      6
       
       
      (
      x
      +
      y
      		)
      		  +  
       
       
      5
       
       
      (
      x
      −
      y
      		)
      =
       
       
      2
  • (i)
    (
    (
    -1
    2
    		 )
    ,
    0
    )
  • (ii)
    (
    (
    -1
    4
    		 )
    ,
    0
    )
  • (iii)
    (
    1
    2
    ,
    0
    )
  • (iv)
    (
    (
    -1
    2
    		 )
    ,
    -1
    )
  • (v)
    (
    (
    -1
    2
    		 )
    ,
    -2
    )
Question 20
20.
A train crosses a telegraph post in 23.84 sec and a bridge 668.56 m long in 39.80 sec. What is the length of the train?
  • (i)
    1000.66 m
  • (ii)
    998.66 m
  • (iii)
    997.66 m
  • (iv)
    999.66 m
  • (v)
    996.66 m
Question 21
21.
    • Due to a leak at the bottom, pipe Y takes
    • 10
      2
      7
      hr
    • to fill the tank.
    • The leak alone can empty the full tank in
    • 72
      hr
    • .
    • In what time can pipe Y alone fill the tank when the leak is closed?
  • (i)
    11
    hr
  • (ii)
    10
    hr
  • (iii)
    8
    hr
  • (iv)
    6
    hr
  • (v)
    9
    hr
Question 22
22.
The equation of y-axis is
  • (i)
    y
    =
    x
  • (ii)
    x
    =
    1
  • (iii)
    y
    =
    0
  • (iv)
    x
    =
    0
  • (v)
    y
    =
    1
Question 23
23.
    • Solve the following pair of equations :
    •  
       
      2
       
       
      (
      4
      x
      +
      y
      		)
      		  +  
       
       
      3
       
       
      (
      4
      x
      −
      y
      		)
      =
       
       
      (
      −
      4
      		)
    •  
       
      13
       
       
      (
      4
      x
      +
      y
      		)
      		  −  
       
       
      3
       
       
      (
      4
      x
      −
      y
      		)
      =
       
       
      64
  • (i)
    (
    0
    ,
    (
    -1
    4
    		 )
    )
  • (ii)
    (
    0
    ,
    1
    2
    )
  • (iii)
    (
    1
    ,
    1
    4
    )
  • (iv)
    (
    3
    ,
    1
    4
    )
  • (v)
    (
    0
    ,
    1
    4
    )
Question 24
24.
    • A can do
    • 11
      12
    • of a work in
    • 4
      7
      12
      hr
    • .
    • He works for
    • 2
      hr
    • when B joins him.
    • They work together and complete the work in
    • 1
      3
      4
      hr
    • .
    • In how much time, B alone can do the work?
  • (i)
    6
    hr
  • (ii)
    9
    hr
  • (iii)
    4
    hr
  • (iv)
    8
    hr
  • (v)
    7
    hr
Question 25
25.
A student walks from his house to school at 6.71 kmph and arrives 6.10 min late. The next day he walks at 15.19 kmph and reaches the school 19.30 min before time. What is the distance from his house to school?
  • (i)
    5.09 km
  • (ii)
    6.09 km
  • (iii)
    4.09 km
  • (iv)
    3.09 km
  • (v)
    7.09 km
    Assignment Key
  •  1) (i)
  •  2) (i)
  •  3) (v)
  •  4) (iv)
  •  5) (i)
  •  6) (i)
  •  7) (i)
  •  8) (ii)
  •  9) (v)
  •  10) (iii)
  •  11) (iii)
  •  12) (ii)
  •  13) (iv)
  •  14) (ii)
  •  15) (i)
  •  16) (v)
  •  17) (i)
  •  18) (v)
  •  19) (i)
  •  20) (ii)
  •  21) (v)
  •  22) (iv)
  •  23) (v)
  •  24) (v)
  •  25) (i)