Tag: equations and simple functions

Quizzes (5) Questions (48)

Questions Related to equations and simple functions

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

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

If the sum of four consecutive even integers is $212$, what is the value of the second even integer?

  1. $50$
  2. $51$
  3. $52$
  4. $53$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four consecutive even numbers be $x, x + 2, x + 4$ and $x + 6$.

Therefore, $x + x + 2 + x + 4 + x + 6 = 212$
$4x + 12 = 212$
$4x = 212 - 12$
$4x = 200$ (Divide both sides by $4$)
$x = 50$
The second number be $x + 2$
So, the second number is $52$.

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

If the sum of four consecutive odd integers is $400$, what is the value of the first odd integer?

  1. $95$
  2. $96$
  3. $97$
  4. $98$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four consecutive odd numbers be $x, x + 2, x + 4$ and $x + 6$.
Therefore, $x + x + 2 + x + 4 + x + 6 = 400$
$4x + 12 = 400$
$4x = 400 - 12$
$4x = 388$  (Divide both sides by $4$)
$x = 97$
The first number be $x$ 
So, the first number is $97$.

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

If the sum of four consecutive integers is $110$, what is the value of the third consecutive integer?

  1. $26$
  2. $27$
  3. $28$
  4. $29$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four consecutive numbers be $x, x + 1, x + 2$ and $x + 3$.
Therefore, $x + x + 1 + x + 2 + x + 3 = 110$
$4x + 6 = 110$
$4x = 110 - 6$
$4x = 104$   (Divide both sides by $4$)
$x = 26$
The third number be $x + 2$ 
So, the third number is $28$.

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 sum of a $2$ digit number and the number obtained by reversing its digits is $154$. If the digits differ by $4$, find the number.

  1. $95$
  2. $73$
  3. $84$
  4. $62$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let two digit number $=ab=10a+b$
Sum of number and reversed number $=154$
$(10a+b)+(10b+a)=154$
$a+b=14$
difference between digits$=\left|a-b\right|=4$
$a-b=\pm 4$
$(a+b=14)+(a-b=4)=2a=18$    $a=9,b=5$
$(a+b=14)-(a-b-4)=2a=10$      $a=5,b=9$
$\therefore   \text {Number}=95 (or)59$
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Two numbers are in the ratio $3 : 5$. If $9$ is subtracted from each, the new numbers are in the ratio $12 : 23$. Find the smaller number.

  1. $27$
  2. $33$
  3. $49$
  4. $55$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be $x$ and $y$

$\dfrac{x}{y}=\dfrac{3}{5}$ ...(1)

According to the question,

$\dfrac{x-9}{y-9}=\dfrac{12}{23}$ ...(2)

$x=\dfrac{3y}{5}$

$ \dfrac { \dfrac { 3y }{ 5 } -9 }{ y-9 } =\dfrac { 12 }{ 23 }  $

$  \dfrac { 3y-45 }{ 5y-45 } =\dfrac { 12 }{ 23 } $

$23(3y-45)=12(5y-45)$

$69y-1035=60y-540$

$9y=1035-540=495$

$y=55$

From (1)

$\dfrac{x}{55}=\dfrac{3}{5}$

Thus the smaller number is 33

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 age of Vamsi's sister is $4\dfrac { 1 }{ 2 } $ times that of Vamsi, where as his uncle is $30$ years older than him. If the total of their ages is $56$ years, what is the age of Vamsi?

  1. $12$ years
  2. $10$ years
  3. $8$ years
  4. $4$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the age of Vamsi be $x$.
$\therefore$ age of Vamsi's sister  $=4 \cfrac{1}{2} \times x = \cfrac{9}{2} x$
Age of Vamsi's uncle $= 30 +$ Vamsi's age $= 30 + x$
Given that:-
age of Vamsi's sister $+$ age of Vamsi + age of Vamsi's uncle $= 56$
$\Rightarrow \; x + \cfrac{9}{2} x + 30 + x = 56$
$\Rightarrow \; \cfrac{13}{2} x = 56 - 30$
$\Rightarrow$ $13x = 52$
$\Rightarrow$ $x = 4$
Hence, age of Vamsi is $4$ 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

Deepak bought $12$ oranges for Rs $7.20$. Vimal bought x oranges more than Deepak's for Rs $9.60$. What is the value of x?

  1. $2$
  2. $5$
  3. $4$
  4. $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Deepak bought $12$ oranges for Rs.$7.20$

Thus, cost of one orange =Rs.$\dfrac{7.20}{12}$=Rs $0.60$

Vimal bought $x$ oranges more than Deepak's for Rs.$9.60$

Number of oranges Vimal bought=$\dfrac{9.60}{0.60}=16$

$x$= Number of oranges Vimal bought - Number of oranges Deepak bought

$x=16-12=4$

$x=4$