Tag: solving linear equations with variable on both sides

Questions Related to solving linear equations with variable on both sides

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

In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?

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

  1. $2$

  2. $3$

  3. $4$

  4. $5$

Show answer
Correct Option: B
Explanation:

Let $d$ and $s$ represent the number of daughters and sons respectively.
Then, we have :
$d - 1 = s$ and $2 \left(s - 1\right) = d$.
Solving these two equations, we get: $d = 4$, $s = 3$.

A number consists of two digits whose sum is $9$. If $27$ is added to the number, its digits are interchanged. Are the given steps to find the number true?
Step $1$: Let the unit's digit be x
Step $2$: Then, ten's digit $=(9-x)$
$\therefore$ number $=10\times (9-x)+x\Rightarrow 90-10x+x=(90-9x)$
Step $3$: Adding $27$ to the number $90-9x$ we get $117-9x$
Step $4$: Number with digits interchanged is $10x+(9-x)=9x+9$
Step $5$: $117-9x=9x+9$ 
Step $6$: Therefore unit's digit$=6$ and ten's digit $=3$
Step $7$: Hence the number $=36$.

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

  1. Yes

  2. No

  3. Cannot say

  4. Only step $1$ and $2$ are correct

Show answer
Correct Option: A
Explanation:

All the given steps to find that unknown number are True.
Hence the option A is the correct answer.

When a number is reduced by $4$, it becomes $80\%$ of itself. Find the number.

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

  1. $20$

  2. $30$

  3. $40$

  4. $50$

Show answer
Correct Option: A
Explanation:
Let the Number be $X$
Number is reduced by $4$ i.e. $X-4$.
Now number becomes $80 \% $ of itself
$X-4 =  80\%  $ of $X$
$ \Rightarrow X-4 = \dfrac{80}{100}\times X$
$ \Rightarrow X-4 = 0.8 X$
$ \Rightarrow 0.2X=4 $
$ \Rightarrow X=20 $
The number is $20$.

A number is multiplied by $2\displaystyle\frac{1}{3}$ times itself and then $61$ is subtracted from the product obtained. If the final result is $9200$, then the number is __________.

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

  1. $36$

  2. $63$

  3. $67$

  4. $37$

Show answer
Correct Option: B
Explanation:

Let the number is $x$

According to given question, we have
$ x\times \dfrac{7x}{3} -61 = 9200$

$\Rightarrow \dfrac{7x^2}{3}=9261$
$\Rightarrow x^2=9261\times  \dfrac{3}{7}$
$\Rightarrow x^2 =3969$
$\Rightarrow x=\sqrt{3969}$
$\Rightarrow x=63$

The two consecutive multiples of $3$ whose sum is $51$ are __________.

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

  1. $24, 27$

  2. $20, 31$

  3. $40, 11$

  4. $25, 26$

Show answer
Correct Option: A
Explanation:

Lets say $x$ is the multiple of $3$

Next consecutive multiple of $3$ will be $(x+3)$
Given sum is $=51$
$\Rightarrow x+x+3=51$
$\Rightarrow  2x=48$
$\Rightarrow x=24$
Two consecutive multiples of $3$ are $24,27$.

$\displaystyle\left(\displaystyle\frac{2}{3}\right)^{rd}$ of a number when multiplied by $\displaystyle\frac{3}{4}$ of the same number make $338$. The number is ___________.

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

  1. $18$

  2. $24$

  3. $36$

  4. $26$

Show answer
Correct Option: D
Explanation:

Let the number is $x$

Thus according to given problem, we have
$\dfrac{2}{3} x\times  \dfrac{3}{4} x= 338$
$x^2=338\times 2$
$x^2= 676=26^2$
$x=26$
Therefore, the number is $26$.

A number is multiplied by half of itself and then $32$ is added to the product, if the final result is $130$, then find the original number.

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. $7$

  3. $5$

  4. $14$

Show answer
Correct Option: D
Explanation:

Let the number be $x$

According to given question, we have
$x\times  \dfrac{x}{2} +32=130$

$\Rightarrow \dfrac{x^2}{2}=98$
$\Rightarrow x^2=196$
$\Rightarrow x=14$

Therefore, the number is $14$.