Tag: solving linear equations with variable on both sides

Questions Related to solving linear equations with variable on both sides

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?

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

  1. $43\ yr$

  2. $67\ yr$

  3. $45\ yr$

  4. $69\ yr$

Show answer
Correct Option: A
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. 

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

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

  1. $13$

  2. $17$

  3. $19$

  4. Data inadequate

  5. None of these

Show answer
Correct Option: B
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 $

Solve $3x-450=2x-240$.

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

  1. $210$

  2. $230$

  3. $220$

  4. $200$

Show answer
Correct Option: A
Explanation:

We have,

$3x-450=2x-240$

$3x-2x=450-240$

$x=210$

Hence, this is the answer.

The age of  manoj  after $15$ years is $4$ times the age of that $15$ years before. His present age is 

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

  1. 10 years

  2. 15 years

  3. 20 years

  4. 25 years

Show answer
Correct Option: D
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


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.

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

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

  2. $\dfrac{7}{17}$

  3. $\dfrac{11}{21}$

  4. None of these

Show answer
Correct Option: C
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 $=\dfrac{x}{x+10}=\dfrac{11}{11+10}=\dfrac{11}{21}$

If
$\displaystyle \frac{a}{3y}\, +\, \frac{3b}{x}\, =\, 1$ and $3a + 1 = 2a + 2 $
x = 5, find the value of y.

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

  1. 0.83333

  2. 2.5

  3. 2.0

  4. 1.5

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Correct Option: A

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

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

  1. -4

  2. -2

  3. 3

  4. 5

Show answer
Correct Option: B
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.

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?

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

  1. $7a, 4a$ years

  2. $4a, 10a$ years

  3. $12a, 3a$ years

  4. $15a, 3a$ years

Show answer
Correct Option: A
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 $=4a$.

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

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

  1. $8$

  2. $17$

  3. $64$

  4. $136$

Show answer
Correct Option: D
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$

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

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

  1. $55$ minutes

  2. $52$ minutes $1$ sec

  3. $51$ minutes $12$ sec

  4. $48$ minutes $15$ sec

Show answer
Correct Option: C
Explanation:
Time taken = Volume flown / Volume flown in 1 min

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

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

$=51 min. 12 sec$