2 Marks Questions

Question 12 Marks

If $11$ is subtracted from $4$ times a number, the result is $89$. Find the number.

Answer

Let the required number is $x$ Then, $4x - 11 = 89$ Or, $4x = 89 + 11$
$\Rightarrow\text{x}=\frac{100}{4}$$x = 25$

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Question 22 Marks

Write a statement for the equation, given below: $x - 7 = 14$

Answer

$7$ less than from the number $x$ is $14.$

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Question 32 Marks

A man earns $Rs. 25$ per hour. How much does he earn in $x$ hours?

Answer

Earning of the man per hour $= Rs. 25$ Earning of the man in $x$ hours $= Rs. (25 \times x) = Rs. 25x$

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Question 42 Marks

Verify by substitution that: The root of $8 - 7y = 1$ is $y = 1$

Answer

The given equation is $8 - 7y = 1$
Substituting $y = 1$, we get $L.H.S. = 8 - 7y = 8 - 7 \times 1 = 8 - 7 = 1 = R.H.S.$
Hence, it verified that $y = 1$ is the root of the given equation.

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Question 52 Marks

Reena is $6$ years older than her brother Ajay. If the sum of their ages is $28$ years, what are their present ages?

Answer

Let Ajay's age is $x$ years and Reena's age is $x + 6$ Then, $x + x + 6 = 28$ Or, $2x = 28 - 6$
$\Rightarrow\text{x}=\frac{22}{2}$ $x = 11$
So, the present age of ajay is $11$ and reena is $(11 + 6) = 17$

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Question 62 Marks

Verify by substitution that: The root of $3x - 5 = 7$ is $x = 4$

Answer

The given equation is $3x - 5 = 7$
Substituting $x = 4$, we get $L.H.S. = 3x - 5 = 3 × 4 - 5 = 12 - 5 = 7 = R.H.S$.
It is verified that $x = 4$ is the root of the given equation.

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Question 72 Marks

Find a number which when multiplied by $5$ is increased by $80.$

Answer

Then, $5x = 80 + x$ Or, $5x - x = 80$
$\Rightarrow 4x = 80$
$\Rightarrow\text{x}=\frac{80}{4}$
$x = 20$

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Question 82 Marks

Verify by substitution that:
The root of $3 + 2x = 9$ is $x = 3$

Answer

The given equation is $3 + 2x = 9$
Substituting $x = 3$, we get $L.H.S. = 3 + 2x$
$= 3 + 2 × 3$
$= 3 + 6 = 9$
$= R.H.S.$
It is verified that $x = 3$ is the root of the given equation.

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Question 92 Marks

Verify by substitution that:
The root of $5x - 8 = 2x - 2$ is $x = 2$

Answer

The given equation is $5x - 8 = 2x - 2$
Substituting $x = 2,$ we get
$L.H.S. = 5x - 8$
$=5 × 2 - 8$
$= 10 - 8$
$= 2$
$R.H.S. = 2x - 2$
$= 2 × 2 - 2$
$= 4 - 2$
$= 2$
$L.H.S. = R.H.S.$
Hence, it is verified that $x = 2$, is the root of the given equation.

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Question 102 Marks

The sum of three consecutive natural numbers is $114$. Find the numbers.

Answer

Let the required numbers are, $x, x + 1, x + 2$
Then, $x + x + 1 + x + 2 = 114$
Or, $3x = 114 - 3$
$\Rightarrow\text{x}=\frac{111}{3}$
$x = 37$
So, the numbers are $37, 38$ and $39$

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Question 112 Marks

Verify by substitution that:
The root of $\frac{\text{z}}{7}=8$ is $\text{z}=56$

Answer

The given equation is $\frac{\text{z}}{7}=8$
Substituting the value of z = 56, we get
$L. H. S. =$ $\frac{56}{7}$
$= 8$
$= R.H.S.$
Hence, it is verified that $z = 56$ is the root of the given equation.

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Question 122 Marks

Deepak is twice as old as his brother Vikas. If the difference of their ages be $11$ years, find their present ages.

Answer

Let the age of Vikas is $x$ years and Deepak is $2x$ years
Then, $2x - x = 11$
Or, $x = 11$
So, their present ages are $11$ and $22$ years

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Question 132 Marks

If $9$ is added to a certain number, the result is $36$. Find the number.

Answer

Let the required number is $x$ Then, $x + 9 = 36$
Or, $x = 36 - 9$
$x = 27$

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