Tag: solving linear equations with variable on both sides

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Questions Related to solving linear equations with variable on both sides

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 ratio of the present age of Manoj to that of Wasim is $3:11$. Wasim is $12\ yr$ younger than Rehana. Rehanas age after $7\ yr$ will be $85\ yr$. What is thepresent age of Manojs father, who is $25\ yr$ older than Manoj?

  1. $43\ yr$
  2. $67\ yr$
  3. $45\ yr$
  4. $69\ yr$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

 the present age of Wasim $=11x$

 present age of Manoj $=3x$

 present age of Rehana $=11x+12$
 present age of Manoj's father $=3x+25$

 after $7$ years, Rehana's age is $85$ years. 
 $11x+12+7=85$
 $ 11x=66$
 $x=6$
 
age of Manoj's father $=3 \times  6 + 25 = 43$ 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

The sum of three consecutive odd numbers is $38$ more than the average of these numbers. What is the first number

  1. $13$
  2. $17$
  3. $19$

  4. Data inadequate

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
let $'a'$ be the first odd number

As per Question

$ a+a+2+a+4 = 38 +\dfrac{a+a+2+a+4}{3}$

$ \Rightarrow 3a+6 = 38+a+2 $

$ \Rightarrow 2a = 34$

$ \Rightarrow a = 17 $
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  manoj  after $15$ years is $4$ times the age of that $15$ years before. His present age is 

  1. 10 years

  2. 15 years

  3. 20 years

  4. 25 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of manoj be $x$ years.

According to the question,
$x+15=4(x-15)$
$x+15=4x-60$
$3x=75$
$x=25$ 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

The denominator of a rational number is greater from its numerators by 10. If the numerators is increased by 19 & the denominator is decreased by 1. The number obtained is $\dfrac { 3 }{ 2 } $. Find the rational number.

  1. $\dfrac{1}{11}$
  2. $\dfrac{7}{17}$
  3. $\dfrac{11}{21}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the numerator be $x$.

$\Rightarrow$  Then, denominator will be $=x+10$
According to the question,
$\Rightarrow$ $\dfrac{x+19}{x+10-1}=\dfrac{3}{2}$

$\Rightarrow$  $\dfrac{x+19}{x+9}=\dfrac{3}{2}$

$\Rightarrow$  $2(x+19)=3(x+9)$

$\Rightarrow$  $2x+38=3x+27$

$\Rightarrow$  $x=38-27$

$\Rightarrow$  $x=11$

$\Rightarrow$  The required rational number $=\dfrac{x}{x+10}=\dfrac{11}{11+10}=\dfrac{11}{21}$

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

Given that $\displaystyle {\frac{-6p\, -\, 9}{3}\, =\, \frac{2p\, +\, 9}{5}},$ find the value of p

  1. -4

  2. -2

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We shall Apply cross multiplication method.

$\dfrac { -6p-9 }{ 3 } =\dfrac { 2p+9 }{ 5 } \ \Longrightarrow 5\times \left( -6p-9 \right) =3\times \left( 2p+9 \right) \ \Longrightarrow -30p-6p=27+45\ \Longrightarrow -36p=72\ \Longrightarrow p=-2$
Ans- Option B.

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 boy is now $a$ years old and his father is $5a$ years old. How old will the father be when the boy is $3a$ years old? How old was the father when the boy was born?

  1. $7a, 4a$ years
  2. $4a, 10a$ years
  3. $12a, 3a$ years
  4. $15a, 3a$ years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Difference of the age of boy and father $=5a-a=4a$

$\therefore$ The father's age when the boy is $3a$ years old $=3a+4a=7a$
When the boy was born, then the father's age $=4a$.

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 boy was asked to multiply a given number by $\displaystyle \frac{8}{17}$. Instead, he divided the given number by $\displaystyle \frac{8}{17}$ and got the result $225$ more than what he should have got if he had multiplied the number by $\displaystyle \frac{8}{17}$. The given number was

  1. $8$
  2. $17$
  3. $64$
  4. $136$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the given number be $x$


According to problem, 

$ 225 + x(\cfrac {8}{17}) = \cfrac{x \times 17}{8}$
$ 225 = \cfrac{17x}{8} - \cfrac{8x}{17}$
$ 225 = \cfrac {225x}{136}$
$ x=136$

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

Water flows at the rate of $10$ metres per minute from a cylindrical pipe $5$ mm. in diameter. The time taken to fill up a conical vessel, whose diameter at the base is $40$ cm and depth $24$ cm., is

  1. $55$ minutes
  2. $52$ minutes $1$ sec
  3. $51$ minutes $12$ sec
  4. $48$ minutes $15$ sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Time taken = Volume flown / Volume flown in 1 min

$=\dfrac{\frac{1}{3}P _i(20)^2 \times 24}{P _i \times \frac{2.5}{10} \times 1000}$

$=\dfrac{3200P _i}{62.5P _i}$

$=51 min. 12 sec$