Question 11 Mark
Five times a number increased by $7$ is $27.$
AnswerLet the number be $x.$ Then, five times of number be $5x.$
Since, it is increased by $7$ i.e. $5x + 7$ and it gives result $27.$
Hence, the equation formed is $5x + 7 = 27$
View full question & answer→Question 21 Mark
The length of a rectangle is two times its breadth. Its perimeter is $60\ cm.$
Perimeter in terms of $x$ is _______.
AnswerPerimeter of rectangle $= 2 ($Length $+$ Breadth$) = 2 (2x + x)$
View full question & answer→Question 31 Mark
________ is the solution of the equation $3x - 2 = 7.$
AnswerSolve the given equation for $x, 3x - 2 = 7$
$\Rightarrow 3x = 7 + 2 [$transponding $(-2)$ to $RHS]$
$\Rightarrow 3x = 9$
$\Rightarrow\frac{3\text{x}}{3}=\frac{9}{3} [$dividing both sides by $3]$
$\Rightarrow\text{x}=3$
View full question & answer→Question 41 Mark
In natural numbers, $x - 5 = -5$ has ________ solution.
AnswerSolve the given equation for $x, x - 5 = -5 $
$\Rightarrow x = -5 + 5 [$tranposing $(-5)$ to $RHS] $
$\Rightarrow x = 0$ Since, natural numbers do not contain zero, hence the equation has no solution.
View full question & answer→Question 51 Mark
In a test Abha gets twice the marks as that of Palak. Two times Abha's marks and three times Palak's marks make $280.$ The equation formed is ________.
AnswerTwo times of Abha’s marks $= 2$
$(2x) = Ax$ and three times the Palak marks $= 3(x) = 3x$
Now, two times Abha’s marks and three times Palak’s marks make $280.$
So, the equation formed is $4x + 3x = 280.$
View full question & answer→Question 61 Mark
In a Mathematics quiz, $30$ prizes consisting of $1st$ and $2nd$ prizes only are to be given. $1st$ and $2nd$ prizes are worth $Rs. 2000$ and $Rs. 1000,$ respectively. If the total prize money is $Rs. 52,000$ then show that: The total value of prizes in terms of $x$ are ________.
AnswerTotal value of prizes in terms of $x$ are $2000x + 1000(30 - x).$
View full question & answer→Question 71 Mark
If $3 - x = -4,$ then $x =$ _______.
AnswerGiven that, $3 - x = -4$
$\Rightarrow -x = -4 - 3 [$transposing $3$ to $RHS]$
$\Rightarrow -x = -7$
$\Rightarrow x = 7 [$multiplying both sides by $(-1)]$
View full question & answer→Question 81 Mark
Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the _________ of the term.
AnswerAny term of an equation may be transposed from one side of the equation to the other side of the equation by changing the sign of the term. Solution: Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the sign of the term.
View full question & answer→Question 91 Mark
In a test Abha gets twice the marks as that of Palak. Two times Abha's marks and three times Palak's marks make $280.$ If Palak gets $x$ marks, Abha gets ________ marks.
AnswerIf Palak gets $x$ marks, then Abha gets twice the marks as that of Palak, i.e. $2x,$
View full question & answer→Question 101 Mark
The solution of the equation $x + 15 = 19$ is _________.
AnswerSolve the equation for $x,$
$\Rightarrow x + 15 = 19$
$\Rightarrow x = 19 - 15 [$transposing $15$ to $RHS]$
$x = 4$ Hence, the solution of the given equation is $4.$
View full question & answer→Question 111 Mark
If $4x - 7 = 11,$ then $x = 4.$
AnswerSolve the equation for $x,\Rightarrow4\text{x}-7=11$
$\Rightarrow4\text{x}=11+7 [$transposing $(-7)$ to $RHS]$
$\Rightarrow4\text{x}=18$
$\Rightarrow\frac{4\text{x}}{4}=\frac{18}{4} [$dividing both sides by $4]$
$\text{x}=\frac{9}{2}$
View full question & answer→Question 121 Mark
In a bag there are $5$ and $2$ rupee coins. If they are equal in number and their worth is $Rs. 70,$ then The worth of $x$ coins of $Rs. 5$ each ________.
AnswerNumber of coins of $Rs. 5 = x$
So, the worth of $Rs. 5$ of $x$ coins $= Rs. 5 $
$ x = Rs. 5x$
View full question & answer→Question 131 Mark
If $10$ less than a number is $65,$ then the number is _________.
AnswerLet the number be $x.$
Then, the equation will be $x - 10 = 65$
Now, solving the equation for $x,$
$\Rightarrow x 65 + 10 [$transposing $(-10)$ to $RHS]$
$\Rightarrow x = 75$
Hence, the number is $75.$
View full question & answer→Question 141 Mark
In natural numbers, $4x + 5 = -7$ has ________ solution.
AnswerSolve thr equation for $x,$
$4x + 5 = -7$
$\Rightarrow 4x = -7 - 5 [$transposing $5$ to $RHS]$
$\Rightarrow 4x = -12$
$\Rightarrow x = -3 [$dividing both sides by $3]$
Since, the value of $x$ is not natural number, hence the equation has no solution in natural numbers.
View full question & answer→Question 151 Mark
The sum of two numbers is $60$ and their difference is $30.$ The difference of numbers in term of $x$ is________.
AnswerGiven, one number $= x[$from $(a)]$
Then, other number $= (60 - x)$
$\therefore$ Difference $= (60 - x) - x = 60 - 2x$
View full question & answer→Question 161 Mark
If $\frac{9}{5}\text{x}=\frac{18}{5},$ then $x =$ ______
AnswerGiven that, $\frac{9}{5}\text{x}=\frac{18}{5}$
On dividing both sides by $\frac{9}{5},$ we get
$\Rightarrow\frac{9}{5}\text{x}+\frac{9}{5}=\frac{18}{5}+\frac{9}{5}$
$\Rightarrow\text{x}=\frac{18}{5}\times\frac{5}{9}=2$
View full question & answer→Question 171 Mark
In a Mathematics quiz, $30$ prizes consisting of $1st$ and $2nd$ prizes only are to be given. $1st$ and $2nd$ prizes are worth $Rs. 2000$ and $Rs. 1000,$ respectively. If the total prize money is $Rs. 52,000$ then show that: The solution of the equation is _______.
AnswerFrom $(c),$
$1000x + 30000 = 52000$
$\Rightarrow 1000x = 52000 - 30000 = 22000$
$\Rightarrow\text{x}=\frac{22000}{1000}=22$
View full question & answer→Question 181 Mark
Sum of two numbers is $81.$ One is twice the other. If smaller number is $x$, the other number is _________.
AnswerWe are given that one number is twice the other. If smaller number is $x,$ then the other number is $2x.$
View full question & answer→Question 191 Mark
If $\text{x}-\frac{7}{8}=\frac{7}{8},$ then $x = $________
AnswerGiven equation is $\text{x}-\frac{7}{8}=\frac{7}{8}$
$\text{x}=\frac{7}{8}+\frac{7}{8} [$transposing $\Big(-\frac{7}{8}\Big)$ to $RHS]$
$\text{x}=\frac{7+7}{8} [$taking $LCM]$
$\text{x}=\frac{14}{8}=\frac{7}{4}$
View full question & answer→Question 201 Mark
The sum of two numbers is $60$ and their difference is $30.$ The numbers ________are and _________.
AnswerThe numbers are $x$ and $(60 - x).$ Now, put the value of $x,$ we get
Frist number $= 15$
Second number $= 60 - 15 = 45$
View full question & answer→Question 211 Mark
If $84$ exceeds another number by $12,$ then the other number is ________.
Answer$\Rightarrow 84 - x = 12 $
$\Rightarrow -x = 12 - 84 [$transposing $84$ to $RHS] $
$\Rightarrow -x = -72$
$\Rightarrow x = 72 [$multiplynig both sides by $(-1)]$
Hence, the number is $72.$
View full question & answer→Question 221 Mark
If $\frac{1}{6}-\text{x}=\frac{1}{6},$ then $x =$ ________.
AnswerGiven that, $\frac{1}{6}-\text{x}=\frac{1}{6}$
$\Rightarrow-\text{x}=\frac{1}{6}-\frac{1}{6} [$transposing $\frac{1}{6}$ to $RHS]$
$\Rightarrow-\text{x}=0$
$\Rightarrow\text{x}=0 [$multiplying both sides by $(-1)]$
View full question & answer→Question 231 Mark
One third of a number added to itself gives $10,$ can be represented as $\frac{\text{x}}{3}+10=\text{x}.$
AnswerLet the number be $x.$ Then, the equation formed is $\frac{\text{x}}{3}+\text{x}=10$
View full question & answer→Question 241 Mark
$x - 1 =$ _______ ; when $2x = 2.$
AnswerGiven that, $2\text{x}=2$
$\Rightarrow\frac{2\text{x}}{2}=\frac{2}{2} [$dividing both sides by $2]$
$\Rightarrow\text{x}=1$
$\therefore\text{x}-1=1-1=0$
View full question & answer→Question 251 Mark
Sum of two numbers is $81.$ One is twice the other. The equation formed is _________.
AnswerWe are given that sum of two numbers is $81.$
So, the equation will be $x + 2x = 81$
View full question & answer→Question 261 Mark
If $\text{x}-\frac{1}{2}=-\frac{1}{2},$ then $x =$ ______
AnswerGiven that, $\text{x}-\frac{1}{2}=-\frac{1}{2}$
$\Rightarrow\text{x}=\frac{1}{2}-\frac{1}{2} [$transposing $\Big(-\frac{1}{2}\Big)$ to $RHS]$
$\Rightarrow\text{x}=0$
View full question & answer→Question 271 Mark
If $z + 3 = 5,$ then $z =$ _______.
AnswerSolve the given equation for $z,$
$z + 3 = 5$
$\Rightarrow z = 5 - 3 [$tranponding $3$ to $RHS]$
$\Rightarrow z = 2$
View full question & answer→Question 281 Mark
Finding the value of a variable in a linear equation that _______ the equation is called a _______ of the equation.
Answer Finding the value of a variable in a linear equation that satisfies the equation is called a root of the equation.
Solution:
Finding the value of a variable in a linear equation that satisfies the equation is called a root of the equation.
View full question & answer→Question 291 Mark
$x - 0 =$ _______ ; when $3x = 12.$
AnswerGiven that, $3x = 12$
$\Rightarrow\frac{3\text{x}}{3}=\frac{12}{3} [$dividing both sides by $3]$
$\text{x}=4$
$\therefore\text{x}-0=4-0=4$
View full question & answer→Question 301 Mark
The length of a rectangle is two times its breadth. Its perimeter is $60\ cm.$ The solution of the equation is ________.
AnswerOn driving the equation by $6,$
we get $\frac{6\text{x}}{6}=\frac{60}{6}$
$\Rightarrow\text{x}=10$
Hence, the solution of the equation is $10.$
View full question & answer→Question 311 Mark
Mohan is $3$ years older than Sohan. The sum of their ages is $43$ years.
AnswerLet age of Sohan be $x$ year.
Then, the age of Mohan is $(x + 3)$ year.
$\therefore$ Sum of their ages $= 43$
So, the equation formed is $x + (x + 3) = 43$
View full question & answer→Question 321 Mark
Six times a number is $10$ more than the number.
AnswerLet the number be $x.$
Then, $6$ times of a number $= 6x$
So, the equation formed is $6x = 10 + x$
View full question & answer→Question 331 Mark
________ is the solution of $3x + 10 = 7.$
AnswerSolve the given equation for $x,$
$\Rightarrow 3x + 10 = 7$
$\Rightarrow 3x = 7 - 10 [$transposing $10$ to $RHS]$
$\Rightarrow 3x = -3$
$\Rightarrow\frac{3\text{x}}{3}=\frac{-3}{3} [$dividing both sides by $3]$
$\text{x}=-1$
View full question & answer→Question 341 Mark
If $9$ is the solution of variable $x$ in the equation $\frac{5\text{x}-7}{2}=\text{y,}$ then the value of $y$ is $28.$
AnswerGiven that, $x = 9$ Put the value of $x$ in the equation,
we get $\Rightarrow\frac{5(9)-7}{2}=\text{y}$
$\Rightarrow\frac{45-7}{2}=\text{y}$
$\Rightarrow\frac{38}{2}=\text{y}$
$\Rightarrow\text{y}=19$
View full question & answer→Question 351 Mark
If $2x + 3 = 5,$ then value of $3x + 2$ is ________.
AnswerSolve the given equation for $x,$
$2x + 3 = 5$
$\Rightarrow 2x = 5 - 3 [$transposing $3$ to $RHS]$
$\Rightarrow\frac{2\text{x}}{2}=\frac{2}{2} [$dividing both sides by $2]$
$\Rightarrow\text{x}=1$
View full question & answer→Question 361 Mark
$\frac{9}{5}$ is the solution of the equation $4x - 1 = 8.$
AnswerSolve the equation for $x,$
$\Rightarrow 4x - 1 = 8$
$\Rightarrow 4x = 8 + 1 [$transposing $(-1)$ to $RHS]$
$\Rightarrow 4x = 9$
$\text{x}=\frac{9}{4} [$dividing both sides by $4]$
View full question & answer→Question 371 Mark
In a bag there are $5$ and $2$ rupee coins. If they are equal in number and their worth is $Rs. 70,$ then The worth of $x$ coins of $Rs. 2$ each ________.
AnswerSimilarly, the worth of $12$ of $x$ coins $= Rs. 2x$
View full question & answer→Question 381 Mark
In a test Abha gets twice the marks as that of Palak. Two times Abha's marks and three times Palak's marks make $280.$ Marks obtained by Abha are ________.
AnswerMarks obtained by abha are $2x,$
i.e. $2 \times 40 = 80.$
View full question & answer→Question 391 Mark
$5$ is the solution of the equation $3x + 2 = 17.$
AnswerSolve the equation for $x, 3x + 2 = 17$
$\Rightarrow3\text{x}=17-2[ $transposing $2$ to $RHS]$
$\Rightarrow\frac{3\text{x}}{3}=\frac{15}{3} [$dividing both sides by $3]$
$\Rightarrow\text{x}=5$
View full question & answer→Question 401 Mark
Subtracting $5$ from $p,$ the result is $2.$
AnswerSubtract $5$ from $p$ i.e. $p - 5$ and its results $2.$
Hence, the equation formed is $p - 5 = 2.$
View full question & answer→Question 411 Mark
If a number is increased by $20,$ it becomes $45.$ Then the number is ________.
AnswerLet the number be $x.$
If it is increased by $20,$ it becomes $(x + 20),$
So, the equation formed is $x + 20 = 45$
$\Rightarrow x = 45 - 20 [$transposing $20$ to $RHS]$
$\Rightarrow x = 25 $
Hence, the number is $25.$
View full question & answer→Question 421 Mark
The sum of two numbers is $60$ and their difference is $30.$ The equation formed is______.
AnswerWe are given that difference between two numbers is $30.$
So, the equation formed is $60 - 2x = 30$
$\Rightarrow -2x = 30 - 60 [$transposing $60$ to $RHS]$
$\Rightarrow -2x = -30$
$\Rightarrow 2x = 30 [$multiplying both sides by $(-2)]$
View full question & answer→Question 431 Mark
In a test Abha gets twice the marks as that of Palak. Two times Abha's marks and three times Palak's marks make $280.$ The solution of the equation is ________.
AnswerSolve the equation for $x,$
$\Rightarrow4\text{x}+3\text{x}=280$
$\Rightarrow7\text{x}=280$
$\Rightarrow\frac{7\text{x}}{7}=\frac{280}{7} [$dividing both sides by $7]$
$\text{x}=40$ Hence, the solution of the equation is $40.$
View full question & answer→Question 441 Mark
Sum of two numbers is $81.$ One is twice the other. The numbers are________ and _________.
AnswerThe two number are $x = 27$ and $2x = 2 \times 27 = 54.$
View full question & answer→Question 451 Mark
$x - $________ $= 15;$ when $\frac{\text{x}}{2}=6.$
AnswerGiven that, $\frac{\text{x}}{2}=6$
$\Rightarrow\text{x}=12$
$\therefore12-(-3)=15$
Hence, $\text{x}-(-3)=15$
View full question & answer→Question 461 Mark
In a Mathematics quiz, $30$ prizes consisting of $1st$ and $2nd$ prizes only are to be given. $1st$ and $2nd$ prizes are worth $Rs. 2000$ and $Rs. 1000,$ respectively. If the total prize money is $Rs. 52,000$ then show that: The equation formed is _______.
AnswerThe equation formed is $1000x + 30000 = 52000$ From $(b),$
$2000x + 1000(30 - x) = 52000$
$\Rightarrow 2000x + 30000 - 1000x = 52000$
$\Rightarrow 1000x + 30000 = 52000$
View full question & answer→Question 471 Mark
In a Mathematics quiz, $30$ prizes consisting of $1st$ and $2nd$ prizes only are to be given. $1st$ and $2nd$ prizes are worth $Rs. 2000$ and $Rs. 1000,$ respectively. If the total prize money is $Rs. 52,000$ then show that: The number of $1st$ prizes are and the number of $2nd$ prizes are _______.
AnswerThe number of $1st$ prizes are $22$ and the number of $2nd$ prizes are $8.$
From $(b), 2000x + 1000(30 - x) = 52000$
$2x + (30 - x) = 52 [$dividing both sides by $1000]$
$x + 30 = 52$
$\Rightarrow x = 52 - 30 = 22$
$\therefore$ Number of $2nd$ prizes $= 30 - 22 = 8.$
View full question & answer→Question 481 Mark
If $5$ is added to three times a number, it becomes the same as $7$ is subtracted from four times the same number. This fact can be represented as _________.
AnswerLet the number be $x.$
Now, $5$ is added to $3$ times the number $5 + 3x. $
It is same as $7$ is subtracted from $4$ times the number,
i.e. $Ax - 7.$ So, the equation formed is $5 + 3x = 4x - 7.$
View full question & answer→Question 491 Mark
The sum of two numbers is $60$ and their difference is $30.$ If smaller number is $x,$ the other number is ________ .(use sum)
AnswerIf the smaller number is $x,$ then the other number is $(60 - x),$
since the sum of both numbers is $60.$
View full question & answer→Question 501 Mark
$\frac{3}{2}$ is the solution of the equation $8x - 5 = 7.$
AnswerSolve the equation for $x,$
$\Rightarrow8\text{x}-5=7$
$\Rightarrow8\text{x}=7+5[ $transposing $(-5)$ to $RHS]$
$\Rightarrow8\text{x}=12$
$\Rightarrow\frac{8\text{x}}{8}=\frac{12}{8} [$dividing both sides by $8]$
$\text{x}=\frac{3}{2}$
View full question & answer→