Question 11 Mark
If $6x = 18,$ then $18x = 54.$
AnswerTrue.Solution:
Given, $6x = 18$
$3 \times 6x = 18 \times 3$
$18x = 54$
View full question & answer→Question 21 Mark
$\frac{\text{x}}{5}+30=18$ has the solution as ______.
Answer$\frac{\text{x}}{5}+30=18$ has the solution as $-60.$
Solution:
Given, $\frac{\text{x}}{5}+30=18$
$\frac{\text{x}}{5}=18-30$
$\frac{\text{x}}{5}=-12$
$\frac{\text{x}}{5}\times5=-12\times5$
$\text{x}=-60$
Hence, the solution is $-60.$
View full question & answer→Question 31 Mark
$9x -$ _________ $= -21$ has the solution $(-2).$
Answer$9x - 3 = -21$ has the solution $(-2).$
Solution:
Let $9x - m = -21$ has the solution $(-2).$
Since, $x = -2$ is the solution of the equation.
$9 \times (-2) - m = -21 -18 + 21 = m m = 3$
Hence, $9x - 3 = -21$ has the solution $(-2).$
$-18 - m = -21$
View full question & answer→Question 41 Mark
In the equation $2x = 4 - x,$ transposing $-x$ to $LHS,$ we get $x = 4.$
AnswerFalse.Solution:
Given, $2x = 4 - x = 2x + x = 4 [$transposing $-x$ to $LHS] = 3x = 4$
View full question & answer→Question 51 Mark
The denominator of a rational number is greater than the numerator by $10$. If the numerator is increased by $1$ the and denominator is decreased by $1,$ then expression for new denominator is _________.
AnswerThe denominator of a rational number is greater than the numerator by $10.$ If the numerator is increased by $1$ the and denominator is decreased by $1,$ then expression for new denominator is $x + 9.$
Solution:
Let numerator be $x.$ Then, denominator $= x + 10$
Rational number $=\frac{\text{x}}{\text{x}+10}$
According to question,
New rational number $=\frac{\text{Numerator }+1}{\text{Denominator }-1}$
$\frac{\text{x}+1}{\text{x}+10-1}=\frac{\text{x}+1}{\text{x}+9}$
Hence, the new denominator is $x + 9.$
View full question & answer→Question 61 Mark
In a $2$ digit number, the units place digit is $x.$ If the sum of digits be 9, then the number is $(10x - 9).$
AnswerGiven, unit’s digit $= x$ and sum of digits $= 9$
Ten’s digit $= 9 - x$
Hence, the number $= 10(9 - x) + x = 90 - 10x + x = 90 - 9x$
View full question & answer→Question 71 Mark
Shikha’s present age is $p$ years. Reemu’s present age is $4$ times the present age of Shikha. After $5$ years Reemu’s age will be $15p$ years.
AnswerGiven, Shikha’s present age $= p$ years
Then, Reemu’s present age $= 4\ \times\ ($Shikha’s present age$) = 4p$ years
After $5$ years, Reemu’s age $= (4p + 5)$ years.
View full question & answer→Question 81 Mark
Three consecutive numbers whose sum is $12$ are _________, ________and _________.
AnswerThree consecutive numbers whose sum is $12$ are $3, 4$ and $5.$
Solution:
Let the three consecutive numbers be $x, x + 1$ and $x + 2.$
According to the question, $x + x + 1 + x + 2 = 12$
$3x + 3 = 12$
$3(x + 1) = 12 $
$\frac{3(\text{x}+1)}{3}=\frac{12}{3}$
$x + 1 = 4$
$x = 4 - 1$
$x = 3$
Hence, the consecutive numbers are $3, 3 + 1$ and $3 + 2$
i.e., $3, 4$ and $5.$
View full question & answer→Question 91 Mark
On subtracting $8$ from $x,$ the result is $2.$ The value of $x$ is _________.
AnswerOn subtracting $8$ from $x,$ the result is $2$. The value of $x$ is $10.$
Solution:
Given, $x - 8 = 2$
$x = 8 + 2$
$x = 10$
Hence, the value of $x$ is $10.$
View full question & answer→Question 101 Mark
If the sum of two consecutive numbers is $93$ and one of them is $x,$ then the other number is $93 - x$.
AnswerGiven, one of the consecutive number $= x$
Then, the next consecutive number $= x + 1$
According to the question, $x + x + 1 = 93$
$ 2x = 93 2x = 92$
$\frac{2\text{x}}{2}=\frac{92}{2}$x = 46
Hence, the other consecutive number $= 46 + 1 = 47 = 93 - 46 = 93 - x$
View full question & answer→Question 111 Mark
After $18$ years, Swarnim will be $4$ times as old as he is now. His present age is _________.
AnswerAfter $18$ years, Swarnim will be $4$ times as old as he is now. His present age is $6$ years.
Solution:
Let Swarmin’s present age be $x$ years.
After $18$ years, Swarmin’s age $= (x + 18)$ years
According to the question,
$x + 18 = 4x$
$x - 4x = -18$
$-3x = -18$
$-\frac{3\text{x}}{-3}=-\frac{18}{3}$
$x = 6$
Hence, Swarmin’s present age is $6$ years.
View full question & answer→Question 121 Mark
In a linear equation, the _______ power of the variable appearing in the equation is one.
AnswerIn a linear equation, the highest power of the variable appearing in the equation is one.Solution:
e.g. $x + 3 = 0$ and $x + 2 = 4$ are the linear equations.
View full question & answer→Question 131 Mark
The number of boys and girls in a class are in the ratio $5 : 4.$ If the number of boys is $9$ more than the number of girls, then number of boys is $9.$
AnswerLet the number of boys be $5x$ and the number of girls be $4x.$ According to the question, $-5x - 4x = 9 = x = 9$ Hence, number of boys $= 5 × 9 = 45$
View full question & answer→Question 141 Mark
The solution of the equation $3x - 4 = 1 - 2 x$ is _________.
AnswerThe solution of the equation $3? – 4 = 1 – 2$ $x$ is $1.$
Solution:
Given, $3x - 4 = 1 - 2x$
$3x + 2x = 1 + 4$
$5x = 5$
$\frac{5\text{x}}{5}=\frac{5}{5}x = 1$
Hence, the solution of the given equation is $1.$
View full question & answer→Question 151 Mark
A term of an equation can be transposed to the other side by changing its _________.
AnswerA term of an equation can be transposed to the other side by changing its sign.
Solution:
e.g. $x + a = 0$ is a linear equation.
$= x = -a$
Hence, the term of an equation can be transposed to the other side by changing its sign.
View full question & answer→Question 161 Mark
In the equation $3x - 3 = 9,$ transposing $-3$ to $RHS,$ we get $3x = 9.$
AnswerGiven, $3x - 3 = 9$
$= 3x = 9 + 3 [$transposing $-3$ to $RHS]$
$= 3x = 12$
View full question & answer→Question 171 Mark
Any value of the variable which makes both sides of an equation equal is known as a _________ of the equation.
AnswerAny value of the variable which makes both sides of an equation equal is known as a $x = 1$ of the equation.
Solution:
e.g. $x + 2 = 3 = x = 3 - 2 = 1 [$transposing $2$ to $RHS]$
Hence, $x = 1$ satises the equation and it is a solution of the equation.
View full question & answer→Question 181 Mark
If $\frac{\text{x}}{11}=15,$ then $\text{x}=\frac{11}{15}$
AnswerGiven, $\frac{\text{x}}{11}=15$
$x = 11 \times 15$
View full question & answer→Question 191 Mark
If $x$ is an even number, then the next even number is $2(x + 1).$
AnswerGiven, $x$ is an even number. Then, the next even number is $(x + 2).$
View full question & answer→Question 201 Mark
$9$ is subtracted from the product of $p$ and $4$, the result is $11$. The value of $p$ is _________.
Answer$9$ is subtracted from the product of $p$ and $4$, the result is $11.$ The value of $p$ is $5.$
Solution:
Given, $9$ is subtracted from the product of $p$ and $4.$
Then, $4p - 9 = 11$
$4p = 11 + 9$
$4p = 20$
$\frac{4\text{p}}{4}=\frac{20}{4}$ $\text{p}=5$Hence, the value of $p = 5$
View full question & answer→Question 211 Mark
If $\frac{15}{8}-7\text{x}=9,$ then $-7\text{x}=9+\frac{15}{8}.$
AnswerFalse.Solution:
Given, $\frac{15}{8}-7\text{x}=9$ $-7\text{x}=9-\frac{15}{8}$
View full question & answer→Question 221 Mark
$A$ and $B$ are together $90$ years old. Five years ago $A$ was thrice as old as $B$ was. Hence, the ages of $A$ and $B$ five years back would be $(x - 5)$ years and $(85 - x)$ years respectively.
AnswerLet the age of $A$ be $x$ years. Then, age of $S = (90 - x)$ years Five years ago,
the age of $A = (x - 5)$ years
The age of $B = 90 - x - 5 = (85 - x)$ years
Hence, the ages of $A$ and $8$ ve years back would be $(x - 5)$ years and $(85 - x)$ years, respectively.
View full question & answer→Question 231 Mark
Convert the statement Adding $15$ to $4$ times $x$ is $39$ into an equation _________.
AnswerConvert the statement Adding $15$ to $4$ times $x$ is $39$ into an equation $4x + 15 = 39.$
Solution:
$4x + 15 = 39$
To convert the given statement into an equation, first $x$ is multiplied by $4$ and then $15$ is added to get the result $39.$
$i.e. 4x + 15 = 39$
View full question & answer→Question 241 Mark
When a number is divided by $8, $ the result is $-3.$ The number is _________.
AnswerWhen a number is divided by $8,$ the result is $-3.$ The number is $-24.$
Solution:
Let the number be $x.$
According to the question,
$\frac{\text{x}}{8}=-3$
$x = 8 \times (-3)$
$x = -24$
Hence, the required number is $-24.$
View full question & answer→Question 251 Mark
The sum of two consecutive multiples of $10$ is $210$. The smaller multiple is _________.
AnswerThe sum of two consecutive multiples of $10$ is $210.$ The smaller multiple is $100.$
Solution:
Let the two consecutive multiplies of $10$ be $10x$ and $10x + 10.$
According to the question,
$10x + 10x + 10 = 210$
$20x + 10 = 210$
$20x = 210 - 10$
$20x = 200$
$\frac{20\text{x}}{20}=\frac{200}{20}$
$x = 10$
Hence, the smaller multiple is $10 \times 10$ is $100.$
View full question & answer→Question 261 Mark
The solution of the equation $2\text{y}=5\text{y}-\frac{18}{5}$ is _______.
Answer The solution of the equation $2\text{y}=5\text{y}-\frac{18}{5}$ is $\frac{6}{5}$ Solution:
Given, $2\text{y}=5\text{y}-\frac{18}{5}$
$2\text{y} - 5\text{y} =-\frac{18}{5}$
$-3\text{y} =-\frac{18}{5}$
$-\frac{3\text{y}}{-3}=\frac{18}{-3\times5}$ $ \text{y} =\frac{6}{5}$ Hence, the solution of the given equation is $\frac{6}{5}$. View full question & answer→Question 271 Mark
Two different equations can never have the same answer.
AnswerTwo different equations may have the same answer. e.g.
$2x + 1 = 2$ and $2x - 5 = -4$
are the two linear equations whose solution is $\frac{1}{2}.$
View full question & answer→Question 281 Mark
Sum of the ages of Anju and her mother is $65$ years. If Anju’s present age is $y$ years then her mother’s age before $5$ years is $(60 - y)$ years.
AnswerGiven, Anju’s present age $= y$ years
Then, Anju’s mother age $= (65 - y)$ years
Before $5$ years, Anju’s mother age $= 65 - y - 5 = (60 - y)$ years.
View full question & answer→Question 291 Mark
If $\frac{2}{5}\text{x}-2=5-\frac{3}{5}\text{x}$, then $x =$ ________.
AnswerIf $\frac{2}{5}\text{x}-2=5-\frac{3}{5}\text{x}$, then $x = 7.$
Solution:
Given, $\frac{2}{5}\text{x}-2=5-\frac{3}{5}\text{x}$
$\frac{2\text{x}}{5}+\frac{3\text{x}}{5}=5+2$
$\frac{5\text{x}}{5}=7$
$\text{x}=7$
Hence, the value of $x = 7$
View full question & answer→Question 301 Mark
If $\frac{\text{x}}{3}+1=\frac{7}{15},$ then $\frac{\text{x}}{3}=\frac{6}{15}$
AnswerFalse.Solution:
Given, $\frac{\text{x}}{3}+1=\frac{7}{15}$ $\frac{\text{x}}{3}=\frac{7}{15}-1$ $\frac{\text{x}}{3}=\frac{7-15}{15}$ $\frac{\text{x}}{3}=-\frac{8}{15}$
View full question & answer→Question 311 Mark
The share of A when $Rs. 25$ are divided between $A$ and $B$ so that A gets $Rs. 8$ more than $B$ is ______.
AnswerThe share of $A$ when $Rs. 25$ are divided between $A$ and $B$ so that $A$ gets $Rs. 8$ more than $B$ is $Rs. 16.5.$
Solution:
Let $B’s$ share be $Rs. x.$ Then, $A’s$ share $= Rs. (x + 8)$
According to the question,
$x + x + 8 = 25$
$2x + 8 = 25$
$2x = 25 - 8$
$2x = 17$
$\frac{2\text{x}}{2}=\frac{17}{2}$
$x = 8.5$
Hence, $A’s$ share $= 8.5 + 8 = Rs. 16.5$
View full question & answer→Question 321 Mark
The perimeter of a rectangle is $240\ cm.$ If its length is increased by $10\%$ and its breadth is decreased by $20\%,$ we get the same perimeter. Find the length and breadth of the rectangle.
AnswerGiven, one number $= x$ & other number $= 40 - x$
Let $(40 - x) > x$ Then, according to the question,
$40 - x + 8 = 3(x + 8) $
$48 - x = 3x + 24 -x - 3x $
$= 24 - 48 -4x = -24$
$\text{x}=-24\times\Big(-\frac{1}{4}\Big)$
$x = 6$
Hence, one number $x = 6$
& other number $= 40 - x = 40 - 6 = 34$
Now, difference between numbers $= 34 - 6 = 28 \neq 40$
which is not satisfy the condition given in question.
View full question & answer→