Tag: maths

Questions Related to maths

Compute the approximate value of $x$: $\sqrt [3]{\dfrac {2x + 3}{5}} = \dfrac {2}{3}$

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

  1. $-0.76$

  2. $-0.69$

  3. $-0.67$

  4. $0.69$

  5. $0.76$

Show answer
Correct Option: A
Explanation:
Given is $\sqrt [ 3 ]{ \dfrac { 2x+3 }{ 5 }  } = \dfrac { 2 }{ 3 } $
Now raising the power to $3$ on both sides, we get
$\dfrac { 2x+3 }{ 5 } = { (2/3) }^{ 3 }\\ \Rightarrow \dfrac { 2x+3 }{ 5 } =\dfrac { 8 }{ 27 } \\ \Rightarrow 54x+81=40\\ \Rightarrow x=-0.76$

If $\dfrac{3}{9}=\dfrac{3}{x+2}$, 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. $-\dfrac{5}{9}$

  2. $\dfrac{7}{3}$

  3. $3$

  4. $7$

  5. $\dfrac{25}{3}$

Show answer
Correct Option: D
Explanation:

Given, $\dfrac {3}{9}=\dfrac {3}{x+2}$

On cross multiplying, we get
$\Rightarrow 3(x+2)=9(3)$
$\Rightarrow x=9-2$
$\Rightarrow x=7$

The square roots of Radhas and Krishs ages have a sum of $7$ and a difference of $1$. If Radha is older than Krish, how old is Radha?

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

  1. $13$

  2. $4$

  3. $9$

  4. $16$

Show answer
Correct Option: D
Explanation:

Let the ages of Radha and krish be $x^{2}$ and $y^{2}$ respectively

Then square roots of their age will be $x$ and $y$ respectively.

Then according to the question,

$x+y=7$ ..(1)

$x-y=1$...(2)

Adding (1) and (2)

$2x=8$

$x=4$

From (1)

$4+y=7$

$y=3$

Therefore $x^{2}=16$ and $y^{2}=9$

As radha is older,hence age of radha is 16years.

What is the solution of $\displaystyle \frac{x-5}{2} - \frac{x-3}{5} = \frac{1}{2}$?

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

  1. $x = 5$

  2. $x = 7$

  3. $x = 8$

  4. $x = 9$

Show answer
Correct Option: C
Explanation:

Given ,$\dfrac{x-5}{2}-\dfrac{x-3}{5}=\dfrac{1}{2}$

$\dfrac{5x-25-2x+6}{5\times 2}=\dfrac{1}{2}$

$3x-19=5$

$3x=24$

$x=8$

If $x=\displaystyle\frac{1}{\displaystyle 2-\frac{1}{\displaystyle 2-\frac{1}{2-x}}}, (x\neq 2)$, then the value of x is ________?

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

  1. $1$

  2. $3$

  3. $2$

  4. $5$

Show answer
Correct Option: A
Explanation:

$x=\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x}}}$


$\Rightarrow x=\dfrac{1}{2-\dfrac{2-x}{3-2x}}$


$\Rightarrow x=\dfrac{3-2x}{4-3x}$

On solving, we get $x=1$
So, Option (A)

Meera bought packs of trading cards that contain $10$ cards each. She gave away $7$ cards.
$x=$ Number of packs of trading cards
Which expression shows the number of cards left with Meera?

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

  1. $10x-7$

  2. $7x-8$

  3. $5-10x$

  4. $8-5x$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  We have given, $x$ is number of packs of trading cards.

$\Rightarrow$  Pack of trading cards contain $10$ cards each.
$\therefore$    Total number of cards = $10x$
$\Rightarrow$  From total cards she gave away $7$ cards. 
$\therefore$    Number of cards left with Meera = $10x-7$

Solve for x : $\dfrac{(x + 2)(2x - 3) - 2x^2 + 6}{x - 5} = 2.$

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

  1. $5$

  2. $10$

  3. $15$

  4. $\frac{20}{3}$

Show answer
Correct Option: B
Explanation:

$\dfrac{(x+2)(2x-3)-2x^2+6}{x-5}=2$


$\Rightarrow\dfrac{(2x^2+x-6)-2x^2+6}{x-5}=2$

$\Rightarrow\dfrac{x}{x-5}=2$

$\Rightarrow x=2x-10$

$\Rightarrow x=10$.  $[B]$

The present ages of a father and his son are in the ratio $7 : 3$ and the ratio of their ages will be $2 : 1$ after $10 $ years. Then, the present age of father (in years) is -

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

  1. $42$

  2. $56$

  3. $70$

  4. $77$

Show answer
Correct Option: C
Explanation:

Let the present ages of father and son be $7x$ and $3x$.

After $10$ years, their ages will be $7x+10$ and $3x+10$.
According to the question, we have
$\dfrac {7x+10}{3x+10}=\dfrac {2}{1}$
$1(7x+10)=2(3x+10)$
$7x+10=6x+20$
$7x-6x=20-10$
$x=10$
Then present age of father is $7x$, i.e. $7\times 10=70$ years.

A number when added to its half gives $36$. Find the number.

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

  1. $24$

  2. $28$

  3. $20$

  4. $18$

Show answer
Correct Option: A
Explanation:

Let the number be $x$

$\Rightarrow x+\cfrac { x }{ 2 } =36\ \Rightarrow \cfrac { 3x }{ 2 } =36\ \Rightarrow x=24$

$A$ has certain amount in his account. He gives half of this to his eldest son and one third of the remaining to his youngest son. The amount left with him now is

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

  1. $\cfrac { 1 }{ 3 } $ of the original

  2. $\cfrac { 2 }{ 5 } $ of the original

  3. $\cfrac { 3 }{ 4 } $ of the original

  4. $\cfrac { 1 }{ 6 } $ of the original

Show answer
Correct Option: A
Explanation:

$x-\cfrac { 1 }{ 2 } -\cfrac { 1 }{ 6 } x=\cfrac { 1 }{ 3 } x$