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Let us assume that the number of notes of Rs. $10$be x then we have to find the number of notes of Rs. $20$.So we can write,

$

\Rightarrow {\text{x + number of 20Rs}}{\text{. notes = 50}} \\

\Rightarrow {\text{Number of 20 Rs}}{\text{. notes = 50 - x}} \\

$

Now we know the number of notes so we can find the values of the notes,

The value of x notes of$10$ Rs.$ = 10 \times {\text{x = 10x}}$

The value of ($50 - {\text{x}}$) notes of Rs.$20$ $ = 20 \times \left( {50 - {\text{x}}} \right)$

Now since the total sum is Rs.$800$.Then,

$ \Rightarrow $ Value of x notes of$10$ Rs. + value of ($50 - {\text{x}}$) notes of Rs.$20$= $800$

$ \Rightarrow 10{\text{x + 20}}\left( {50 - {\text{x}}} \right) = 800$

On simplifying the above equation, we get

$ \Rightarrow 10{\text{x + 1000 - 20x = 800}}$

On multiplying the eq. with (-) sign we get,

$ \Rightarrow - 10{\text{x + 20x - 1000 = - 800}}$

On separating the variable x and the constant values, we get

$ \Rightarrow 20{\text{x - 10x = 1000 - 800}}$

On solving we get,

$ \Rightarrow 10{\text{x = 200}} \Rightarrow {\text{x = }}\dfrac{{200}}{{10}} = 20$

So, we get the number of notes of Rs. $10$=$20$. Then the number of notes of Rs. $20$=$50 - 20 = 30$