Tag: equations and rearranging formulae

Questions Related to equations and rearranging formulae

Arvind has Piggybank. It is full of one-rupee and fifty paise coins. It contains $3$ times as many fifty paise coins as one rupee coins. The total amount of money in the bank is $Rs\ 35$. How many one-rupee and fifty paise coins are there in the bank ?(respectively)

maths equations and rearranging formulae further equations solving linear equations with variable on both sides equations and simple functions

  1. $14,\ 42$

  2. $15,\ 42$

  3. $14,\ 52$

  4. None of these

Show answer
Correct Option: A
Explanation:

Let no. of fifty paise coins be $x$ and no.of one Rupees coins be $y$

then $x=3y$

According to question 
$0.50 \times x+1 \times y=35\$
$\Rightarrow 0.5x+y=35\$
$\Rightarrow 0.5 \times 3y+y=35\$
$1.5y+y=35\$
$\Rightarrow 2.5y=35\$
$\Rightarrow y=\dfrac{350}{25}\$
$\Rightarrow y=14\$
So,
    $x=3y\$
$=3 \times 14\$
$=42$

Therefore no.of fifty paise coins is $42$ ans no.of one Ruppee coin is $14$.

Sum of the ages of three friends $x$ years ago was $y$ years. Then what will be the sum of their ages now?

maths equations and rearranging formulae further equations solving linear equations with variable on both sides equations and simple functions

  1. $3x+y$

  2. $x+3y$

  3. $3x-y$

  4. $x-3y$

Show answer
Correct Option: A
Explanation:

Let their present age be $a,b,c$


Sum of their present age $=a+b+c$

Their ages $x$ years ago $a-x,b-x,c-x$

Sum $=a+b+c-3x$

Given $a+b+c-3x=y$

$a+b+c=y+3x=3x+y$


So option $A$ is correct.