3 Marks Question

Question 13 Marks

Write two equations for which $2$ is the solution.

Answer

Let the two numbers be $x$ and $y,$ which has solution $2$ in equation.
$a.\ $For getting first equation, the number $x$ is multiplied by $2$, then the number is $2x$.
After that, $3$ is subtracted from it which results into $1$.
Hence, $2x - 3 = 1$
$2x = 3 + 1$ [transposing $-3$ to $RHS]$
$\Rightarrow 2x = 4$
$\Rightarrow\frac{2\text{x}}{2}=\frac{4}{2}$
$\Rightarrow x = 2$ [dividing both sides by $2]$
$b.\ $For getting second equation, the number $y$ is multiplied by $3$, then the number is $3y$. After that, it will be added to $4$ which results into $10.$
Hence, $3y + 4 = 10$
On solving, $3y = 10 - 4$
$\Rightarrow 3y = 6$ [transposing $+4$ to $RHS$]
$\Rightarrow\frac{3\text{y}}{3}=\frac{6}{3}$ [dividing both sides by $3]$
$\Rightarrow y = 2$
Hence, two equations are
$2x - 3 = 1$ and $3y + 4 = 10.$

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Question 23 Marks

Sunita is half the age of her mother Geeta. Find their ages,
$i.\ $After $4$ years?
$ii.\ $Before $3$ years?

Answer

Let the age of Sunita’s mother $= 2x yr$
Then, according to the question,
Sunita’s age $=\big(\frac{1}{2}\big) \times $ Age of Sunita’s mother $=\frac{2\text{x}}{2}$
$i.\ $After $4yr,$
Sunita’s age $= (x + 4)yr$
$\therefore$ Her mother’s age $= (2x + 4)yr$
Note After $4$ years means, $4$ years is added in present age.
$ii.\ $Before $3yr,$
Sunita’s age $= (x - 3)yr$
and her mother’s age $= (2x - 3)yr$
Note: Before $3$ years means, $3$ years is subtracted from present age.

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Question 33 Marks

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

Answer

According to the question,
Number of tanks to collect rain water $= 8$
Rain water collected in per tank (in $L$) $= x$
Then, total rain water in tanks (in $L$) = Number of tanks $x$ Rain water collected per tank $= 8 \times x = 8x$
But in the one tank, already $100L$ of water exist,
Then, total amount of water in the tank $= 100$ + [Total rain water in $L$] $= (100 + 8x)$

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Question 43 Marks

Write an equation whose solution is not a whole number.

Answer

We know that, whole numbers are $0, 1, 2, 3, …$
Now, let the one number be $x$ whose solution is not a whole number.
For getting equation, the number $x$ will be added to $1$ which results into $0$.
Then,
$x + 1 = 0$ [transposing +$1$ to $RHS$]
On solving $x = -1$
which is not a whole number.
Hence, required equation is $x + 1 = 0.$
In questions $75$ to $84,$ change the statements, converting expression into statements in ordinary language.

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Question 53 Marks

Two consecutive odd integers.

Answer

Any odd integer can be written as $2n + 1$, where n is an integer.
So, next odd integer will be $(2n + 1) + 2$, i.e. $2n + 3$.
Hence, two consecutive odd integers are $2n + 1$ and $2n + 3.$
Note: A sequence of consecutive even or odd integer is a list of two or more integers which increase by $2$ from one integer to the next consecutive integer. They have a difference of $2$ between every two integers.

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