NCERT Exemplar Solutions For Class 6 Maths Chapter 11 Algebra

Class 6 Maths Chapter 11 Algebra

Question 1. If each matchbox contains 50 matchsticks, the number of matchsticks required to fill n such boxes is

1. 50 + n
2. 50n
3. 50 ÷ n
4. 50 – n

Solution: (2): Number of matchsticks in one box = 50

The number of matchsticks required to fill n boxes = 50 x n = 50n

Question 2. Amulya is x years of age now. 5 years ago her age was

1. (5 -x) years
2. (5 +x) years
3. (x- 5) years
4. (5 ÷ X) years

Solution: (3): The present age of Amulya is x years.

Question 3. Which of the following represents 6 x x

1. 6x
2. \(\frac{x}{6}\)
3. 6+x
4. 6-x

Solution: (1): 6 x x can be represented as 6x.

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Question 4.  Which of the following is an equation?

1. x + 1
2. x – 1
3. x – 1=0
4. x+1 >0

Solution:(3): Equation means an expression with a variable, constants and the sign of equality (=).

x- 1 = 0 is an equation.

Question 5. If x takes the value 2, then the value of + 1 0 is

1. 20
2. 12
3. 5
4. 8

Solution:(2) : When we put x = 2 in the given expression x + 10, we get

x + 10 = 2 + 10 = 12.

Question 6. If the perimeter of a regular hexagon is x metres, then the length of each of its sides is

1. (x + 6) metres
2. (x ÷ 6 ) meters
3. (x- 6) metres
4. (6 ÷ x) metres

Solution: (2): Perimeter of a regular hexagon

= 6 x Length of each side

⇒ x m = 6 x Length of each side

⇒ Length of each side = (x + 6) m

Question 7. Which of the following equations has = 2 as a Solution?

1. x + 2 = 5
2. x – 2 = 0
3. 2x + 1 =0
4. x + 3 = 6

Solution: (2) : (A) Putting x = 2 in x + 2, we get 2+2=4*5

Putting x = 2 in x- 2, we get 2- 2 = 0

Putting x = 2 in 2x + 1, we get 2×2+l=5*0

Putting x = 2 in x + 3, we get 2 + 3 = 5* 6

Thus, the above conditions shows that x = 2 is the solution of x- 2 = 0

Question 8. For any two integers x and y, which of the following suggests that the operation of addition is commutative?

1. x + y = y + x
2. x + y > x
3. x – y = y – x
4. x x y = y x x

Solution: (A): x + y- y + x shows that addition is commutative.

Question 9. Which of the following equations does not have a solution in integers?

1. x + 1 =1
2. x – 1 =3
3. 2x+ 1 =6
4. 1 -x = 5

Solution: (3) : (A) x +1 =1

x + 1- 1 = 1 – 1

[Subtracting1 from both sides]

⇒ x = 0, which is an integer

x-1 =3

⇒ x-l + l= 3 + 1 [Adding1 to both sides]

⇒  x = 4, which is an integer.

2x +1 = 6

⇒ 2x + 1- 1 =6- 1

[Subtracting1 from both sides]

2x = 5

⇒ \(\frac{2 x}{2}=\frac{5}{2}\) [Dividing both sides by 2]

⇒ \(x=\frac{5}{2} \text {, }\) which is not an integer.

1 -x = 5

1-x-l =5-1

[Subtracting1 from both sides]

⇒ -x = 4

⇒ -(-x) =-4

[Multiplying both sides by (-1)]

⇒ x = -4, which is an integer

Thus, the above conditions show that equation 2x + 1 = 6 does not have a solution in integers.

Question 10. In algebra, an x b means ab, but in arithmetic 3×5 is

1. 35
2. 53
3. 15
4. 8

Solution: (3) : 3 x 5 means 15.

Question 11. In algebra, letters may stand for

1. known quantities
2. Unknown quantities
3. Fixed numbers
4. None of these

Solution: (2): In algebra, letters may stand for unknown quantities.

Question 12. “Variable” means that it

1. Can take different values
2. Has a fixed value
3. Can take only 2 values
4. Can take only three values

Solution: (1): “Variable” means that it can take different values.

Question 13. 10 -x means

1. 10 is subtracted x times
2. x is subtracted 10 times
3. x is subtracted from 1 0
4. 10 is subtracted from x

Solution: (3): 10- x means x is subtracted from 10.

Question 14. Savitri has a sum of ₹ x. She spent ₹ 1000 on groceries,₹ 500 on clothes and ₹ 400 on education, and received ₹ 200 as a gift. How much money (in ₹) is left with her?

1. x – 1700
2. x – 1900
3. x + 200
4. x – 2100

Solution: (1):

Given

Savitri has a sum of ₹ x. She spent ₹ 1000 on groceries,₹ 500 on clothes and ₹ 400 on education, and received ₹ 200 as a gift.

Amount of money Savitri has = ₹ x.

Amount of money spent by her =₹ (1000 + 500 + 400) = ₹ 1900

Amount of money received by her as a gift = ₹ 200

Amount of money left with her

= ₹(x- 1900 + 200)

= ₹ (x- 1700)

Question 15. The perimeter of the triangle shown in the given figure is

1. 2x+y
2. x + 2y
3. x + y
4. 2x-y

Solution: (1): The perimeter of the triangle = Sum of all sides

=x+x+y

= 2x + y

Question 16. The area of a square with each side x is

1. xxx
2. 4x
3. x + x
4. 4 = x + x

Solution: (1) : The area of a square = (side) x (side) =x*x

Question 17. The expression obtained when x is multiplied by 2 and then subtracted from 3 is

1. 2x- 3
2. 2x + 3
3. 2x- 3
4. 3x- 2

Solution : x is multiplied by 2 and then subtracted from 3 =3-2 x * x = 3-2x

Question 18. \(\frac{q}{2}=3\) has a solution

1. 6
2. 8
3. 3
4. 2
5. Solution: (1): We have, \(\frac{q}{2}=3\) Multiplying both sides by 2, we get

⇒ \(\Rightarrow \quad \frac{q}{2} \times 2=3 \times 2\)

q = 6

Question 19. x-4 =- 2 has a solution

1. 6
2. 2
3. -6
4. -2

Solution:(2) : We have, x- 4 =-2

⇒  x -4 + 4 = -2 + 4

[Adding 4 to both sides]

⇒  x = 2

Question 20. \(\frac{4}{2}=2\) denotes a V

1. Numerical equation
2. Algebraic expression
3. Equation with a variable
4. False statement

Solution: (1): \(\frac{4}{2}=2\) denotes a numerical equation.

Question 21. Kanta has p pencils in her box. She puts q more pencils in the box. The total number of pencils with her is.

1. p+q
2. PQ
3. p-q
4. \(\frac{p}{q}\)

Solution: (1): Kanta has p pencils in her box. After putting q more pencils in the box, she has a total number of pencils = p + q.

Question 22. The equation 4x = 16 is satisfied by the following value of x

1. 4
2. 2
3. 12
4. -12

Solution:(1) : We have, 4x = 16

⇒ \(\frac{4 x}{4}=\frac{16}{4}\)

x = 4

Question 23. I think of a number and on adding 13 to it, I get 27. The equation for this is

1. x – 27 = 13
2. x – 13 = 27
3. x + 27 = 13
4. x + 13 = 27

Solution: (D): Let the number be x.

According to the question, x + 13 = 27

Question 24. The distance (in km) travelled in h hours at a constant speed of 40 km per hour is_______.
Solution: 40 h : Distance = Speed * Time = (40 x h) km = 40 h km

Question 25. p kg of potatoes are bought for ₹70. The cost of 1 kg of potatoes (in ₹) is_______.
Solution:

⇒ \(\frac{70}{p}\) : The cost of p kg of potatoes = ₹ 70

The cost of1 kg of potatoes = \(₹ \frac{70}{p}\)

Question 26. An auto rickshaw charges ₹ 10 for the first kilometre then ₹ 8 for each such subsequent kilometre. The total charge (in ₹) for d kilometres is_______.
Solution:

Given

An auto rickshaw charges ₹ 10 for the first kilometre then ₹ 8 for each such subsequent kilometre.

2 + 8d: For the first kilometre, rickshaw charges = ₹ 10.

And the charges for subsequent kilometres = ₹ 8.

The charges for d kilometres

= 10 + (d- 1)8

= 10 +8d-8 = 2 + 8d

Question 27. lf 7x + 4 = 25, then the value of x is_______.
Solution: 3:

We have given, 7x + 4 = 25

⇒  7x + 4- 4 = 25- 4

[Subtracting 4 from both sides]

⇒ \(\frac{7 x}{7}=\frac{21}{7}\)

⇒  x = 21

⇒  x = 3

Question 28. The solution of equation 3x + 7 = -20 is _______.
Solution:

-9 : We have, 3x + 7 =- 20

3x + 7- 7 =- 20- 7

[Subtracting 7 from both sides]

⇒  3x = -27

[Dividing both sides by 3]

⇒  x = -9

Question 29. ‘exceeds by 7’ca can be expressed as_______.
Solution: x = y + 7: x exceeds y by 7 can be expressed as = y + 7 or x-y = 7.

Question 30. ‘8 more than three times the number x7 can be written as_______.
Solution: 3x + 8 : 8 more than three times the number x can be expressed as 3x + 8

Question 31. Many pencils bought for? x at the rate of ₹ 2 per pencil is_______.
Solution: \(\frac{x}{2}\) Number of pencils bought for ₹ 2 =1

Number of pencils bought for ₹ x = \(\frac{1}{2} \times x=\frac{x}{2}\)

Question 32. The number of days in w weeks is_______.
Solution: 7W : Number of days in a week = 7

Number of days in w weeks = 7 * w = 7w

Question 33. Annual salary at r rupees per month along with a festival bonus of? 2000 is_______.
Solution: ₹ (12r + 2000) : We have given, monthly salary = ₹ r

Annual salary = ₹ (12 * r) = ₹ 12r

Now, total annual salary with a festive bonus = ₹ (12r + 2000)

Question 34. The two-digit number whose ten digit is Y and unit’s digit is’ is_______.
Solution: + u: The digit at the unit’s place is V.

And the digit at ten’s place is Y.

The number can be expressed as 10 x t + u = lOf + u

Question 35. The variable used in the equation 2p +8 = 18 is _______.
Solution: p : p is the variable in the equation Ip + 8 = 18

Question 36. x metres = _______centimeters.
Solution:

x : 1 metre = 100 cm

⇒  x metres = lOOx cm

Question 37. p litres = _______.millilitres.
Solution:

lOOOp : 1 litre = 1000 millilitres

⇒ p litres = lOOOp millilitres

Question 38. r rupees = _______ paise.
Solution:

Floor : 1 rupee = 100 paise

⇒  r rupees = lOOr paise

Question 39. If their present age of Ramandeep is n years, then her age after 7 years will be_______.
Solution:

(n + 7) years: Present age of Ramandeep = n years

Her age after 7 years = (n + 7) years

Question 40. If I spend f rupees from 100 rupees, the money left with me is_______rupees.
Solution:

100 – f: I have 100 rupees and spend f rupees.

Money left with me = (100 -f) rupees 40.

Question 41. 0 is a solution of the equation x+ 1 = 0
Solution: False

We have given, x +1 = 0

⇒  — 1 – 0- 1

[Subtracting 1 from both sides]

⇒  x –1, which is the solution of the given equation.

Question 42. The equations x + 1 = 0 and 2x + 2 = 0 have the same solution.
Solution: True

We have given, x + 1 = 0

⇒  x +1 -1 =0-1

[Subtracting 1 from both sides]

⇒  x = —1 …(1)

and 2x + 2 = 0

2x + 2-2 = 0-2

[Subtracting 2 from both sides]

⇒  2x = -2

⇒ \(\frac{2 x}{2}=\frac{-2}{2}\)

[Dividing both sides by 2]

⇒  x =-1 …(2)

Thus, (1) and (2) imply that both equations have the same solution.

Question 43. If m is a whole number, then 2m denotes a multiple of 2.
Solution: True

Question 44. The additive inverse of an integer x is 2x.
Solution: False

Since the additive inverse of x is -x.

Question 45. If x is a negative integer, – x is a positive integer.
Solution: True

The negative of a negative integer is always a positive integer.

Question 46. 2x- 5 > 1 1 is an equation.
Solution: False

Since an equation includes a sign of equality(=)

Question 47. In an equation, the LHS is equal to the RHS.
Solution: True

Question 48. In the equation 7k- 7 = 7, the variable is 7.
Solution: False

Since, in the equation 7k-7 = 7, the variable is k.

Question 49. a = 3 Is a solution of the equation 2a- 1 = 5
Solution: True

We have, 2a- 1 = 5

⇒  2n- 1 +1 = 5 + 1

[Adding 1 to both sides]

⇒  2a = 6

⇒  \(\frac{2 a}{2}=\frac{6}{2}\) [Dividing both sides by 2]

⇒  a = 3, which is the solution of the given equation

Question 50. The distance between New Delhi and Bhopal is not a variable.
Solution: True

Question 51. t minutes are equal to 60f seconds.
Solution: True

Since, 1 minute = 60 seconds

t minutes = 60 x f seconds = 60f seconds

Question 52. x = 5 is the solution of the equation 3x + 2 = 20
Solution: False

⇒  3x + 2- 2 = 20- 2

[Subtracting 2 from both sides]

⇒  3x = 18

⇒  \(\quad \frac{3 x}{3}=\frac{18}{3}\) [Dividing both sides by 3]

⇒  x = 6, which is the solution of the given equation.

Question 53. ‘One-third of a number added to itself gives 8’, can be expressed as\(\frac{x}{3}+8=x\)
Solution: False

Let the number be x.

One third of the number = \(\frac{x}{3} \text {. }\)

According to the given question, \(\frac{x}{3}+x=8\)

Question 54. The difference between the ages of the two sisters Leela and Yamini is a variable.
Solution: False

The difference between the ages of the two sisters will be a fixed number.

Question 55. The number of lines that can be drawn through a point is a variable. ,
Solution: False

Question 56. One more than twice the number.
Solution:

Let the number be x.

Twice the number = 2x.

Now, 1 more than 2x can be expressed as 2x + l.

Question 57. 20°C less than the present temperature.
Solution:

Let the present temperature be t°C.

Now, 20°C less than t = (t- 20)°C

Question 58. The successor of an integer.
Solution:

Let the integer be n.

Now, the successor of the integer n = n +1.

Question 59. The perimeter of an equilateral triangle, if the side of the triangle is m.
Solution: We have given, the side of the equilateral triangle = m.

The perimeter of an equilateral triangle

= 3 x side

= 3 m

Question 60. Area of the rectangle with length k units and breadth n units.
Solution:

We have given, a rectangle of length = k units and breadth = n units.

Area of the rectangle = length * breadth = (k x n) sq units = kn sq units

Question 61. Omar helps his mother 1 hour more than his sister does.
Solution:

Let Omar’s sister help her mother for x hours.

Omar helps his mother for (x +1) hours.

Question 62. Two consecutive odd integers.
Solution: Two consecutive odd integers are (2n + 1) and (2n + 3), where n is any integer.

Question 63. Two consecutive even integers.
Solution: Two consecutive even integers are 2m and 2m + 2, where m is any integer.

Question 64. Multiple of 5.
Solution:

A multiple of 5 can be expressed as 5n, where n is an integer.

Question 65. The denominator of a fraction is 1 more than its numerator.
Solution:

Let the numerator of the fraction be x.

The denominator of the fraction can be expressed as x + 1.

The fraction \(=\frac{x}{x+1}\)

Question 66. The height of Mount Everest is 20 times the height of the Empire State Building.
Solution:

Let the height of the Empire State Building be y.

Height of Mount Everest = 20y.

Question 67. If a notebook costs ₹ p and a pencil costs ₹ 3, then the total cost (in ₹) of two notebooks and one pencil.
Solution:

The cost of a notebook = ₹ p

Cost of 2 notebooks = ₹ 2p.

The cost of a pencil =₹ 3.

Cost of two notebooks and one pencil = ₹(2p + 3)

Question 68. Z is multiplied by 3 and the result is subtracted from 1 3.
Solution:

z multiplied by -3 = -3z

– 3z subtracted from 13 =13- (-3z) = 13 + 3z

Question 69. p is divided by 11 and the result is added to 1 0.
Solution:

p divided by 11 = \(\frac{p}{11} .\)

\(\frac{p}{11}\) added to 10 = \(\frac{p}{11}+10 .\)

Question 70. x times 3 is added to the smallest natural number.
Solution: x times of 3 = 3x

And the smallest natural number =1.

So, 3x added to1 = 3x + 1.

Question 71. 6 times q is subtracted from the smallest two-digit number.
Solution:

6 times q = 6q.

The smallest two-digit number = 10

6q subtracted from 10 = 10- 6q.

Question 72. Write two equations for which 2 Is the solution.
Solution: The required equations are 3i/ + 4 = 10 and 2. V- 3 = 1, i.e., for both equations, 2 is the solution.

Question 73. Write an equation for which 0 is a solution.
Solution: The required equation is 2f + 3 = 3, which has solution t = 0.

Question 74. Write an equation whose solution is not a whole number.
Solution: The required equation is x + 1 = 0, and its solution is x = -1, which is not a whole number.

Question 75. A pencil costs? p and a pen cost 5p.
Solution: A pen costs 5 times the cost of a pencil.

Question 76. Leela contributed ₹ y towards the Prime Minister’s Relief Fund. Leela is now left with ₹ (y+ 10000).
Solution: The amount left with Leela is? 10,000 more than the amount she contributed towards the Prime Minister’s Relief Fund.

Question 77. Kartik is n years old. His father is In years old.
Solution: The age of Kartik’s father is seven times the age of Kartik.

Question 78. The maximum temperature on a day in Delhi was p°C. The minimum temperature was (P-10)°C.
Solution: The minimum temperature on a day in Delhi was 10°C less than the maximum temperature.

Question 79. John planted two plants last year. His friend Jay planted 2f + 1 0 plants that year.
Solution: Last year Jay planted 10 more plants than twice the plants planted by his friend John.

Question 80. Sharad used to take p cups of tea a day. After having some health problems, he takes p – 5 cups of tea a day.
Solution: Sharad reduced the consumption of tea per day by 5 cups after having some health problems.

Question 81. The number of students dropping out of school last year was m. Number of students dropping out of school this year is m- 30.
Solution: The number of students dropping out this year is 30 less than the number of students who dropped out last year.

Question 82. The price of petrol was ₹ p per litre last month. The price of petrol now is ₹ (p- 5) per litre.
Solution: The price of petrol per litre decreased this month by 5 than its price last month.

Question 83. Khader’s monthly salary was P in the year 2005. His salary in 2006 was ₹ (P + 1 000).
Solution: Khader’s monthly salary increased by? 1000 in the year 2006 than that of 2005.

Question 84. The number of girls enrolled in a school last year was g. The number of girls enrolled this year in the school is 3g- 1 0.
Solution: The number of girls enrolled this year is 10 less than 3 times the girls enrolled last year.

Question 85. Translate each of the following statements into an equation, using x as the variable:

1. 13 subtracted from twice a number gives 3.
2. One-fifth of a number is 5 less than that number.
3. Two-thirds of the number is 12.
4. 9 added to twice a number gives 1 3.
5. 1 subtracted from one-third of a number gives 1.

Solution:

Let the number be x.

Twice of the number x = 2x

According to question, 2x- 13 = 3

Let the number be x.

One-fifth of the number x = \(\frac{x}{5}.\)

5 less than the number x = x- 5

According to question, \(\frac{x}{5}=x-5\)

Let the number be x.

Two-thin! of the number x \(=\frac{2}{3} x\)

According to question, \(\frac{2}{3} x=12\)

Let the number be x.

Twice of the number x = 2x.

Now, 9 is added to 2x = 9 + 2x

According to the question, 9 + 2x = 13.

Let the number be x.

One-third of the number x = \(\frac{x}{3}\)

Now, 1 is subtracted from \(\frac{x}{3}=\frac{x}{3}-1\)

According to question, “\(\frac{x}{3}-1=1 \text {. }\)

Question 86. Translate each of the following statements into an equation :

• The perimeter (p) of an equilateral triangle is three times its side (a).
• The diameter (d) of a circle is twice its radius (r).
• The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned.
• Amount (a) is equal to the sum of principal (p) and interest (/).

Solution:

We have given the perimeter of an equilateral triangle

= 3 (the side of an equilateral triangle)

⇒  p = 3a

We have given the diameter of a circle

= 2 (the radius of the circle)

⇒  d = 2r

We have given, Selling price = cost price + profit

⇒  s = c + p

We have given, Amount = principal + interest

⇒  a = p + i

Question 87. Let Kanika’s present age be x years. Complete the following table, showing the ages of her relatives:

Solution:

We have given the present age of Kanika = x years.

Her brother’s age = (x- 2) years

Her father’s age = (x + 35) years

Her mother’s age = (x + 35- 3) years = (x + 32) years

Her grandfather’s age = 8x years

Question 88. If m is a whole number less than 5, complete the table and by inspection of the table, find the solution of the equation 2m- 5 = -1 :

Solution:

Given

If m is a whole number less than 5, complete the table and by inspection of the table

For m = 0, 2m-5=2×0-5=0-5=-5

For m = 1, 2m-5=2xl-5=2-5=-3

For m = 3, 2m-5=2×3-5=6-5=l

For m = 4, 2m-5=2×4-5=8-5=3

Thus, the solution of the equation 2m- 5 =-1 is m = 2.

Question 89. A class with p students has planned a picnic. 50 per student is collected, out of which ₹ 1800 is paid in advance for transport. How much money is left with them to spend on other items?
Solution:

Given

A class with p students has planned a picnic. 50 per student is collected, out of which ₹ 1800 is paid in advance for transport.

Number of students in the class = p

The total amount collected from p students =₹ 50p

Amount paid in advance for transport =₹ 1800

The amount left with them = ₹ (50p- 1800)

Question 90. In a village, there are 8 water tanks to collect rainwater. On a particular day, x litres of rainwater is collected per tank. If 100 litres of water was already there in one of the tanks, what was the total amount of water in the tanks on that day?
Solution:

Given

In a village, there are 8 water tanks to collect rainwater. On a particular day, x litres of rainwater is collected per tank. If 100 litres of water was already there in one of the tanks

Number of water tanks = 8

Rainwater collected by each tank = x litres

Rainwater collected by 8 tanks = 8x litres

But 100 litres of water was already there in one of the tanks.

Total amount of water in the tanks = (8x + 100) litres.

Question 91. What is the area of a square whose side is m cm?
Solution:

We have given, the side of a square = m cm

Area of the square = side x side = m x m sq cm

Question 92. The perimeter of a triangle is found by using the formula P = a + b + c, where a, b and c are the sides of the triangle. Write the rule that is expressed by this formula in words.
Solution:

Given

The perimeter of a triangle is found by using the formula P = a + b + c, where a, b and c are the sides of the triangle.

The perimeter of a triangle is the sum of all its sides.

Question 93. The perimeter of a rectangle is found by using the formula P = 2 (I + w), where l and w are respectively the length and breadth of the rectangle. Write the rule that is expressed by this formula in words.
Solution:

Gien

The perimeter of a rectangle is found by using the formula P = 2 (I + w), where l and w are respectively the length and breadth of the rectangle.

The perimeter of a rectangle is twice the sum of its length and breadth.

Question 94. On my last birthday, I weighed 40 kg. If I put on m kg of weight after a year, what is my present weight?
Solution:

Given

On my last birthday, I weighed 40 kg. If I put on m kg of weight after a year

Present weight = weight on last birthday + weight put on after a year.

D 40 kg + tn kg

= (40 + m) kg

Question 95. Length and breadth of rcm and tern, respectively.

1. What will be the length (in cm) of the aluminium strip required to frame the board, if 1 0 cm extra strip is required to fix it properly?
2. Ifx nails are used to repair one board, how many nails will be required to repair 15 such boards?
3. If 500 sq cm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?
4. What will be the expenditure for making 23 boards if the carpenter charges? x per board.

Solution:

We have given, the length of the board = r cm and breadth = t cm.

The length of the aluminium strip to frame the board = Perimeter of the board

= 2(length + breadth)

= 2(r + t) cm

But a 10 cm extra strip is required to fix it properly.

The total length of the aluminium strip = 2(r + t) cm + 10 cm.

Number of nails required to repair 1 board = x.

Number of nails required to repair 15 boards = 15 x  x = 15 x.

The area of the cloth required for the board

= Area of the board

= length x breadth

= r cm x t cm

= (rt) sq cm

The area of the cloth required for 8 boards

= 8 x (rt) sq cm

= 8rt sq cm

But 500 sq cm extra cloth per board is required to cover the edges.

For 8 boards we need 8 x 500 sq cm = 4000 sq cm extra cloth.

Thus, the total area of the cloth required = (8rt + 4000) sq cm

The carpenter charges for 1 board = %x.

The carpenter charges for 23 boards = ?(23*x) = ?23x

Question 96. Sunita is half the age of her mother Geeta. Find their ages

1. After 4 years.
2. Before 3 years.

Solution:

Let the present age of Sunita be x years.

The present age of her mother Geeta = 2(Sunita’s present age) = 2x years.

1.  After 4 years,

Sunita’s age = (x + 4) years

Geeta’s age = (2x + 4) years

2.  Before 3 years,

Sunita’s age = (x- 3) years

Geeta’s age = (2x- 3) years.

Question 97. Match the items of Column I with that of Column 2:
Solution:

(1)⇒ (B), (2) ⇒(E), (3) ⇒ (C), (4) ⇒ (C), (5) ⇒ (A)

The number of comers of a quadrilateral is 4, i.e., a constant.

The variable in the equation 2p + 3 =5 is p.

We have given, x + 2 = 3

⇒ x+2-2=3-2

[Subtracting 2 from both sides]

⇒ x = 1, which is the solution of the given equation.

We have given, 2p + 3 = 5

⇒ 2p + 3 — 3 =5- 3

[Subtracting 3 from both sides]

⇒ 2p = 2

⇒ \(\frac{2 p}{2}=\frac{2}{2}\)

[Dividing both sides by 2]

p = 1, which is the solution of the given equation.

The equality sign (=) is used in an equation