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

Find the value of $y$ in the equation : 
$\displaystyle \frac{(2-3y)+4y}{9y-(8y+7)}=\frac{4}{5}$

  1. $18$
  2. $9$
  3. $-38$
  4. $-32$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\displaystyle \frac{(2-3y)+4y}{9y-(8y+7)}=\frac{4}{5}$
$\Rightarrow \displaystyle \frac{2+y}{y-7}=\frac{4}{5}$

$\Rightarrow 5(2+y)=4(y-7) $ ....( cross multiplying )
$\Rightarrow 10+5y=4y-28$
$\Rightarrow y=-38$
Hence,. the solution is $x=-38$

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

A combination of locks requires 3 numbers to open. The second number is $\displaystyle 2d + 5$ greater than the first number. The third number is $\displaystyle 3d - 20$ less than the second number. The sum of the three numbers is $\displaystyle 10d + 9$. The first number is 

  1. $\displaystyle 5d-11$
  2. $\displaystyle 3d-7$
  3. $\displaystyle 2d+19$
  4. $\displaystyle 3d-11$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the first number be $x$
Then, second number = $x + 2d + 5$
Third number = $x + 2d + 5 -(3d -20)$ = $x -d + 25$
Sum of the three numbers = $ x + x+2d + 5 + x - d +25$ = $ 3x + d +30$

Thus, $ 3x + d +30$ = $10d + 9$
$3x = 10d + 9 - d - 30$ = $9d - 21$
$x = 3d - 7$

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

If $\displaystyle \sqrt{\left ( x-1 \right )\left ( y+2 \right )}=7$, $x$ and $y$ being positive whole numbers, then the values of $x$ and $y$ are, respectively

  1. $8,5$
  2. $15,12$
  3. $22,19$
  4. $6,8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ \sqrt{(x-1)(y+2)}=7\Rightarrow (x-1)(y+2)=7^{2}$
$ \Rightarrow (x-1)=7:and:(y+2)=7$
$ x=8$ and $\displaystyle y=5$

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

$\displaystyle \sqrt{6+\sqrt{6+\sqrt{6+...}}}$ equals 

  1. $\displaystyle 6^{\frac{2}{3}}$

  2. 6
  3. $\displaystyle 6^{\frac{1}{3}}$

  4. 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let  $ x =\sqrt{6+\sqrt{6+\sqrt{6+...}}}$


sqare it on both sides


$x^2=\sqrt{6+\sqrt{6+\sqrt{6+...}}} = 6+x$


$\Rightarrow x^2=6+x $


$\Rightarrow x^2-x-6=0 $


$\Rightarrow x^2-3x+2x-6=0 $


$\Rightarrow x(x-3)+2(x-3)=0 $


$\Rightarrow (x-3)(x+2)=0 $


$either  x-3=0---> x=3 $


$ or  x+2=0 ----> x=-2 $


since result of sqrt of anything will be positive only, therefore,


Answer $x=3$





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

If $\displaystyle \frac{x^2\, -\, (x\, +\, 1)(x\, +\, 2)}{5x\, +\, 1}\, =\, 6$, then $x$ is equal to

  1. $\displaystyle \frac{8}{33}$
  2. $\displaystyle \frac{8}{3}$
  3. $\displaystyle \frac{-8}{33}$
  4. $\displaystyle \frac{-6}{33}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\displaystyle \frac{x^2\, -\, (x\, +\, 1)(x\, +\, 2)}{5x\, +\, 1}\, =\, 6$
$\Rightarrow x^2\, -\, (x^2\, +\, 3x\, +\, 2)\, =\, 6(5x\, +\, 1)$, .....(on cross multiplying )
$\Rightarrow x^2\, -\, x^2\, -\, 3x\, -\, 2\, =\, 30x\, +\, 6$
$\Rightarrow -3x - 2 = 30x + 6$
$\Rightarrow -3x - 30x = 6 + 2 \Rightarrow -33x = 8$
$\Rightarrow x\, =\, \displaystyle \frac{-8}{33}$
Hence, the solution is, $x=-\cfrac{8}{33}$.

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

After receiving two successive raises Hrash's salary became $\dfrac {15}{8}$ times of his initial salary. By how much percent was the salary raised the first time if the second raise was twice as much as high (in percent) as the first ?

  1. $15 \%$
  2. $20 \%$
  3. $25 \%$
  4. $30 \%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial salary was Rs. $100$
After two raise it become $\dfrac {15}{8}$ i.e. $\dfrac {(15 \times 100) }{ 8} =$ Rs. $187.5$
Raise $= 187.5 - 100 = 87.5$
Using formula,
[( first raise  + second raise) + (first raise * 2nd raise) / 100]  = 87.5
$x + 2x +\dfrac { (2x ^2)}{100} = 87.53$
$300x + 2x ^2 = 8750$
$x ^2 + 150x = 4375$
$x ^2 + 150x - 4375 = 0$
$x ^2 + 175x - 25x - 4375 = 0$
$x = -175, 25$ .....(Negative value is not possible)
So, $x= 25\%$
Second raise was $2x = 2 \times 25 = 50\%$.