Tag: maths

Questions Related to maths

If $a\neq 0$ and $\dfrac{5}{x}=\dfrac{5+a}{x+a}$, what is the value of $x$?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $-5$

  2. $-1$

  3. $5$

  4. $2$

Show answer
Correct Option: C
Explanation:

Given:

$a$ $\neq$ $0$ and $\dfrac {5}{x}$ $=$ $\dfrac {5 \space + \space a}{x \space + \space a}$
To find the value of $x$,
$\Rightarrow \dfrac {5}{x}$ $=$ $\dfrac {5 \space + \space a}{x \space + \space a}$
$\Rightarrow 5$ $\times$ $(x$ $+$ $a)$ $=$ $x$ $\times$ $(5$ $+$ $a)$
$\Rightarrow 5x$ $+$ $5a$ $=$ $5x$ $+$ $xa$
Get the co-efficients of $'x'$ on one-side,
$\Rightarrow 5x$ $+$ $xa$ $-$ $5x$ $=$ $5a$
$\Rightarrow xa$ $=$ $5a$
As $(a$ $\neq$ $0)$,    $x$ $=$ $5$
Therefore, the value of $'x'$ is $'5'$.

If one-third of a two digit number exceeds its one-fourth by $8$, then what is the sum of the digits of the number?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $6$

  2. $13$

  3. $15$

  4. $17$

Show answer
Correct Option: C
Explanation:

$(10x + y)\left (\dfrac {1}{3} - \dfrac {1}{4}\right ) = 8$
$\Rightarrow 10x + y = 96$
$\Rightarrow x = 9, y = 6$
$\therefore x + y = 15$

The total cost of three prizes is Rs. $2550$. If the value of second prize is $\left(\displaystyle\frac{3}{4}\right)^{th}$ of the first prize and the value of $3rd$ prize is $\displaystyle\frac{1}{2}$ of the second prize, then the value of the first prize is ___________.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. Rs. $1308$

  2. Rs. $1028$

  3. Rs. $1200$

  4. Rs. $1450$

Show answer
Correct Option: C
Explanation:

let the first,second and third prizes be $x,y$ and $z$ respectively

$x+y+z=2550$.....(1)
$y=\dfrac{3}{4}x$
$z=\dfrac{1}{2}y= \dfrac{3}{8}x$
Putting values of $y$ and $z$ in equation (1)
$x+\dfrac{3}{4}x+\dfrac{3}{8}x=2550$

$\dfrac{8x+6x+3x}{8}=2550$
$17x=2550\times8$
$x=1200$

If $\sqrt {x-1}- \sqrt {x+1}+1 =0$, then $4x$ is equal to ____. 

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $4 \sqrt {-1}$

  2. $0$

  3. $5$

  4. $1 \dfrac {1}{4}$

Show answer
Correct Option: C
Explanation:

We can write it as $\sqrt{x-1} + 1 = \sqrt{x+1}$

Squaring both sides we get,
$x-1 + 1 +2\sqrt{x-1} = x+1$
$\Rightarrow 2\sqrt{x-1} = 1$

Squaring both sides, we get
$4(x-1) = 1$ 
$\therefore 4x = 5$

Solve the following linear equations. If $\cfrac{x-5}{3} = \cfrac{x-3}{5}$, then $x  $is equal to

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $8$

  2. $6$

  3. $2$

  4. $3$

Show answer
Correct Option: A
Explanation:
Given, $\cfrac { x - 5 }{ 3 }  =\cfrac { x-3 }{ 5 }$
Taking L.C.M., we get
$ \cfrac { 5x-25 }{ 15 }  = \cfrac { 3x - 9 }{ 15 } $
$5x - 25 = 3x -9$
Take $x$ terms on one sides and constants on another side, we get
$2x = 16$
$x = 8$

Solve the following linear equations. If $\cfrac{3t-2}{4}-\cfrac{2t+3}{3} = \cfrac{2}{3}-t$, then $t  $ is equal to

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: B
Explanation:
Given $\cfrac { 3t-2 }{ 4 } -\cfrac { (2t+3) }{ 3 }  = \cfrac { 2 }{ 3 }  - t$
L.C.M. of $4,3,3$ is $ 12$
$\Rightarrow  3(3t-2) - 4(2t+3) = 8 - 12t$
$\Rightarrow 9t - 6 -(8t +12) = 8 -12t$
$\Rightarrow t -18  = 8 -12t$
$\Rightarrow 13 t = 26$
$\Rightarrow t = 2$

Solve the following linear equations: $m-\cfrac{m-1}{2} = 1-\cfrac{m-2}{3}$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $m = \cfrac{7}{5}$

  2. $m = \cfrac{2}{3}$

  3. $m = \cfrac{10}{3}$

  4. $m = \cfrac{3}{8}$

Show answer
Correct Option: A
Explanation:
Given, $m - \cfrac { (m-1) }{ 2 }  = 1-\cfrac { (m-2) }{ 3 }$ 
L.C.M. of $2$ and $3$ is $6$
$6m -3(m-1) = 6 - 2(m-2)$
$ 6m - 3m +3 = 6 - 2m +4$
$5m = 7$
$ m = \cfrac { 7 }{ 5 }$

Which of the following is the solution of the equation $\displaystyle \frac{7y+4}{y+2}=\frac{-4}{3}$ ?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $\displaystyle y = -\frac{4}{5}$

  2. $\displaystyle y = \frac{4}{5}$

  3. $\displaystyle y = -\frac{5}{4}$

  4. $\displaystyle y = \frac{5}{4}$

Show answer
Correct Option: A
Explanation:

$\dfrac{7y+4}{y+2}=\dfrac{-4}{3}$
$21y+12=-4y-8$
$25y=-20$
$y=\dfrac{-20}{25} = \dfrac{-4}{5}$

Solve the following equations: $\cfrac{3y+4}{2-6y}=\cfrac{-2}{5}$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $2$

  2. $-4$

  3. $4$

  4. $-8$

Show answer
Correct Option: D
Explanation:

Given, $\dfrac{3y+4}{2-6y}=\dfrac{-2}{5}$

On cross multiplying, we get
$5(3y+4)=-2(2-6y)$
$\Rightarrow 15y+20=-4+12y$
$\Rightarrow 3y=-24$
$\Rightarrow y=-8$

Solve the following equations: $\cfrac{9x}{7-6x}=15$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x = \cfrac{25}{72}$

  2. $x = \cfrac{35}{33}$

  3. $x = \cfrac{45}{39}$

  4. $x = \cfrac{22}{45}$

Show answer
Correct Option: B
Explanation:

Given, $\dfrac{9x}{7-6x}=15$
$9x=105-90x$

Add $90x$ on both the sides, we get
$9x+90x=105-90x+90x $
$99x=105$
$\therefore x=\dfrac{105}{99}=\dfrac{35}{33}$