Tag: maths

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Questions Related to maths

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

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

  1. $-0.76$
  2. $-0.69$
  3. $-0.67$
  4. $0.69$
  5. $0.76$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given is $\sqrt [ 3 ]{ \dfrac { 2x+3 }{ 5 }  } = \dfrac { 2 }{ 3 } $
Now raising the power to $3$ on both sides, we get
$\dfrac { 2x+3 }{ 5 } = { (2/3) }^{ 3 }\\ \Rightarrow \dfrac { 2x+3 }{ 5 } =\dfrac { 8 }{ 27 } \\ \Rightarrow 54x+81=40\\ \Rightarrow x=-0.76$
Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

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?

  1. $13$
  2. $4$
  3. $9$
  4. $16$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $1$
  2. $3$
  3. $2$
  4. $5$
Reveal answer Fill a bubble to check yourself
A Correct answer
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)

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

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?

  1. $10x-7$
  2. $7x-8$
  3. $5-10x$
  4. $8-5x$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 = $10x-7$

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

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 -

  1. $42$
  2. $56$
  3. $70$
  4. $77$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

$A$ 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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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