Sarath has twenty, two rupee and five rupee coins, which totals $~55~$ rupees.
Let $~x~$ be the number of two rupee coins and $~y~$ be the number of five rupee coins Sarath has.
$1)\quad$ express the given information in $~2~$ equations.
$2)\quad$ how many of each type of coin does he have?
On
You already understand why $x+y=20$, since the total number of coins Sarath has is $20$.
For the second equation, note that to get the total value of the two-rupee coins, we multiply its denomination ($2$ rupees) by the number of coins ($x$ coins). So the total value of two-rupee coins is $2$ times $x=2x$.
Likewise, the total value of five-rupee coins is $5$ times $y=5y$.
Altogether, she has $2x+5y$ rupees in total, but the question says $55$. Therefore, $2x+5y=55$.
To answer part two of your question, we have the simultaneous equations: \begin{cases} x+y=20.........................(1) \\ 2x+5y=55.....................(2) \end{cases} Multiply the equation $(1)$ by $2$ to get: $$2x+2y=40........................(3)$$ Subtracting (3) from (2) then yields: $$3y=15$$ $$y=5$$ And substituting $y=5$ into equation (1) gives $x=15$.
Therefore, Sarath has $15$ two-rupee coins and $5$ five-rupee coins.
The total is $55$ Rupees. If all the $5$ coins are turned to $2$ coins, the new total is $2\times20=40$, i.e. a reduction by $15$ Rupees. This reduction corresponds to five coins being depreciated by $5-2=3$ Rupees.
$$15\times2+5\times5.$$