Tag: maths

Questions Related to maths

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

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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

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

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

$=51 min. 12 sec$

In a caravan  in addition to 50 hens there are 45 goats and 8 camels with some keepers.  If the total number of feet be 224 more then the number of heads in the caravan, find the number of keepers

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

  1. 5

  2. 8

  3. 10

  4. 15

Show answer
Correct Option: D
Explanation:

If the number of keepers be x  then total number of feet = $2  \times 50 + 4   \times 45 + 4 \times  8 + 2x$
$=2x + 312$
Total number of heads = $50 + 45 + 8 + x$
$=103 + x$
$\displaystyle \therefore 2x+312=103+x+224$ or$x = 15$

The solution of $\displaystyle 2^{3x-6} =\frac{1}{8^x}$ is---

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

  1. 1

  2. $\displaystyle \frac{4}{2}$

  3. 4

  4. -1

Show answer
Correct Option: A
Explanation:

$\displaystyle 2^{3x-6} =\frac{1}{8^x} ; 2^{3x-6}$
          $\displaystyle = 2^{-3x}$
$3x - 6 = -3x ; x = 1$

Solve $1.32y + 0.02y = 1.19 + y$.

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

  1. $-\dfrac{7}{2}$

  2. $3\dfrac{1}{2}$

  3. $\dfrac{7}{4}$

  4. $-3\dfrac{1}{4}$

Show answer
Correct Option: B
Explanation:

$1.32y+0.02y=1.19+y$

$\Rightarrow 1.34y=1.19+y$
$\Rightarrow 0.34y=1.19$
$\Rightarrow y= \dfrac {1.19}{0.34}$

$\Rightarrow y= \dfrac {119}{34}$

$\Rightarrow$ $ y= \dfrac {7}{2}$ $= 3 \dfrac{1}{2}$