Tag: maths

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Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The difference of two numbers is $72$ and the quotient obtained by dividing one by the other is $3$. Find the numbers.

  1. $36$ $and$ $108$
  2. $16$ $and$ $88$
  3. $63$ $and$ $135$
  4. $\text{none}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Let\>the\>numbers\>be\>x\>and\>y,\>then\>x-y=72\\and\>(\frac{x}{y})=3\\or\>x\>=\>3y\\\therefore\>3y-y=72\\2y=72\\\therefore\>y=36,\>then\>x\>=\>108$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

In an orchard, $\dfrac{1}{5}$ are orange trees, $\dfrac{3}{13}$ are mango trees and the rest are banana trees.  If the banana trees are $148$ in number, find the total number of trees in the orchard.

  1. $252$
  2. $360$
  3. $260$
    <span class="MathJax"><span class="math">
  4. $352$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$let \>total \>number\> of \>trees=x \\then \>banana\> trees =148\\x-(\frac{x}{5})-(\frac{3x}{13})=148\\(\frac{65x-13x-15x}{65})= 148\\\therefore x= (\frac{148\times 65}{37})=260$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

At present anil is $1.5$ times of purvis age. $8\ yr$ later, the respective ratio between Anil and Purvis ages will be $25:18$. What is Purvis present age?

  1. $50\ yr$
  2. $28\ yr$
  3. $42\ yr$
  4. $36\ yr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let Present age of Purvis is $x$ then, Age of Anil will be $1.5x$
 After $8 yr$,
                   Age of anil $=1.5x+8$ And Age of Purvis $=x+8$
             $\dfrac{25}{18}=\dfrac{1.5x+8}{x+8}$
                        $x=28$
 So Age of Purvis $=28 yr$
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Solve for $x : \dfrac { x + 2 } { 6 } - \left[ \dfrac { 11 - x } { 3 } - \dfrac { 1 } { 4 } \right] = \dfrac { 3 x - 4 } { 12 }$

  1. $\dfrac { 6 } { 11 }$

  2. 10

  3. 14

  4. 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$\dfrac{x+2}{6}-\left[\dfrac{11-x}{3}-\dfrac{1}{4}\right]=\dfrac{3x-4}{12}$

$\Rightarrow \dfrac{2(x+2)}{12}-\left[\dfrac{4(11-x)}{12}-\dfrac{3}{12}\right]=\dfrac{3x-4}{12}$

$\Rightarrow 2x+4-[44-4x-3]=3x-4$

$\Rightarrow 2x+4-44+3+4x=3x-4$

$\Rightarrow 6x-37=3x-4$

$\Rightarrow 3x=33$

$\Rightarrow x=11$.
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. Find the number, if the difference between its digits is $3$. 

  1. $14$
  2. $25$
  3. $36$
  4. $47$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let one's digit be $x$ and the tens be $x-3$


Number = $10(x-3) +x$ 

Reversed no. = $10x +x-3$ 

$ 7(10(x-3) +x) = 4(x-3 +10x)\ 70x -210 + 7x = 4x -12 +40x\ 33x = 198\ x = 6$ 

Number = $36$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Solve: $\displaystyle \frac{2x\, +\,1}{10}\, -\, \frac{3\, -\, 2x}{15}\, =\, \frac{x\, -\, 2}{6}$.


Hence, find y, if $\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, +\, 1\, = 0$.

  1. $\displaystyle x\, =\, -\frac{7}{5}; \, y\, =\, -\frac{7}{2}$
  2. $\displaystyle x\, =\, -\frac{2}{5}; \, y\, =\, \frac{7}{2}$
  3. $\displaystyle x\, =\, -\frac{6}{5}; \, y\, =\, -\frac{7}{2}$
  4. $\displaystyle x\, =\, -\frac{12}{5}; \, y\, =\, \frac{7}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ \dfrac {2x + 1}{10} - \dfrac {3-2x}{15} = \dfrac {x-2}{6} $

On taking LCM and simplifying, we get

$ \dfrac {6x + 3 - 6 + 4x}{30} = \dfrac {x - 2}{6} $

$ => \dfrac {10x - 3}{30} = x - 2 $


$ => 10x - 3 = 5x - 10 $

$ 5x = -7 $

$ x = -\dfrac {7}{5} $

Now, substituting x in $ \dfrac {1}{x} + \dfrac {1}{y} + 1 = 0 $, we get

$ - \dfrac {5}{7} + \dfrac {1}{y} + 1 = 0 $

$ => \dfrac {1}{y} = - 1 + \dfrac {5}{7} =  - \dfrac {2}{7} $

$ => y = -\dfrac {7}{2} $

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

An altitude of a triangle is five-third the length of its corresponding base. If the altitude is increased by $4 cm$ and the base is decreased by $2 cm$, the area of the triangle remains same. Find the base and the altitude of the triangle.

  1. The base of the triangle is $12 cm$ and altitude is $20 cm$.
  2. The base of the triangle is $4 cm$ and altitude is $34 cm$.
  3. The base of the triangle is $16 cm$ and altitude is $12 cm$.
  4. The base of the triangle is $8 cm$ and altitude is $32 cm$.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let the base of the triangle be $x$ cm. 
Then, the altitude of the triangle $=\cfrac { 5x }{ 3 } $
So, area of the triangle $=\cfrac { 1 }{ 2 } \times base\times altitude$
$=\cfrac { 1 }{ 2 } \times x\times \cfrac { 5 }{ 3 } x\\ =\cfrac { 5 }{ 6 } { x }^{ 2 }$        ...(1)
On increasing the altitude by $4 cm$ and the decreasing base by $2 cm$, the area remains the same.
Therefore, $\cfrac { 1 }{ 2 } \times (x-2)\times \left( \cfrac { 5x }{ 3 } +4 \right) =\cfrac { 5 }{ 6 } { x }^{ 2 }$       ...[using (1)]
$\Longrightarrow \cfrac { 1 }{ 2 } \times (x-2)(\cfrac { 5x+12 }{ 3 } )=\cfrac { 5 }{ 6 } { x }^{ 2 }$
$ \Longrightarrow (x-2)(5x+12)=5{ x }^{ 2 }$
$ \Longrightarrow 5{ x }^{ 2 }-10x+12x-24=5{ x }^{ 2 }$
$ \Longrightarrow 2x-24=0$
$ \Longrightarrow 2x=24$ or $x = 12$.
 Now, altitude of the triangle $=\cfrac { 5x }{ 3 } =\cfrac { 5\times 12 }{ 3 } =20 cm$
Hence, the base of the triangle is $12 cm$ and altitude is $20 cm$.
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Neglecting air resistance, the upward velocity of the water in the stream of a particular fountain is given by the formula $v = -32t + 28$, where $t$ is the number of seconds after the water leaves the fountain. While going upward, the water slows down until at the top of the stream, the water has a velocity of $0$ feet per second. How long does it take a droplet of water to reach the maximum height?

  1. $0.825$ seconds
  2. $0.925$ seconds
  3. $0.875$ seconds
  4. $0.975$ seconds
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $v = -32t + 28$
It is mentioned that at the maximum height, the velocity of water is $0$ feet per second.
Therefore, final velocity $(v) = 0$. 
$\Rightarrow 0=-32t+28$

$\Rightarrow 32t=28$      
$\Rightarrow t=\cfrac { 28 }{ 32 } =0.875$ seconds

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Twelve years hence a person will be four times as he was twelve years ago, then his present age is

  1. $20$ years
  2. $25$ years
  3. $28$ years
  4. $30$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let his present age be $x$
According to problem
$\Rightarrow\;x+12=4\;(x-12)$
$\Rightarrow\;-3x=-48-12$
$\Rightarrow\;3x=60$
$\Rightarrow\;x=20$ years.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

A father is at present three as old as his son . Five years back he was four times as old as his son.  Find the age of his son

  1. 12 years

  2. 15 years

  3. 18 years

  4. 20 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Present age of the son is 'x' years his father's age is 3x
Five year ago:
Son's age = x - 5 and father's age = $3x - 5$
$\displaystyle \therefore 3x-5=4(x-5)$ or x = 15