Tag: maths

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Questions Related to maths

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

$x=16-12=4$

$x=4$

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

Pipes A and B can fill a tank in $18$ minutes and $12$ minutes respectively. If both the pipes are opened simultaneously, how long will they take to fill the tank?

  1. $30$ minutes
  2. $20$ minutes
  3. $10 $ minutes
  4. $7\dfrac{1}{5}$ minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let $'V'$ be total volume of tank
Time taken by $A$ to fill tank $=18 min$
Speed of $A=\dfrac{V}{18}$
Time taken by $B$ to fill tank $=12 min$
Speed of $B=\dfrac{V}{12}$
$\therefore$  Total time taken by $A$  and  $B$  to fill tank when opened
Simultaneously $=\dfrac{V}{(\dfrac{V}{12}+\dfrac{V}{18})}$
$=\dfrac{18\times 12}{30}$
Time taken $= 7.2 min$
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 three non-zero prime numbers is $100$. One of them exceeds the other by $36$. Find the largest number.

  1. $73$
  2. $91$
  3. $67$
  4. $57$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
As we know that the sum of three odd numbers cannot be even.
$\therefore$ one of the prime is even 
Since $2$ is the only prime number which is even.
$\therefore$ one of the three prime numbers is $2$.
Let one of the other prime numbers is ${p} _{1}$ then the third prime number will be ${p} _{1} + 36$. 
Now according to question,
$2 + {p} _{1} + {p} _{1} + 36 = 100$
$2{p} _{1}=62$
$p1=31$

Hence, the three prime numbers are $2, 31$ and $67$ and the largest among them is $67$.
Hence, $67$ is the correct answer.

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 two numbers is $45$ and their difference is $11$. What are the two numbers?

  1. $28$ and $17$
  2. $27$ and $18$
  3. $25$ and $20$
  4. $22$ and $23$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the numbers be $a$ and $b$
Given that 

$a+b=45$ ....(1)
$a-b=11$ ....(2)
Adding these two equations, we get
$2a=56$
$\Rightarrow a=28$
Substituting value of $a$ in equation (1), we get
$28+b=45$
$\Rightarrow b=45-28$
$\Rightarrow b=17$
We get $a = 28$ and $b=17$