Question

# A sum of Rs.$800$ is in the form of denominations of Rs. $10$ and Rs.$20$.If the total number of notes is $50$, then find the number of notes of each type.

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Hint: Assume the number of notes of Rs. $10$ be y then since the total number of notes is $50$ , so the number of notes of Rs. $20$will be $50 - {\text{x}}$.Here total sum of money is Rs.$800$. Add the values of notes of Rs. $10$ and Rs.$20$ and equate it to Rs.$800$.Solve the equation for x. Put the value of x in the number of notes and you’ll get the answer.

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. $20$=$50 - 20 = 30$
Hence, there are$20$ notes of Rs. $10$ and $30$ notes of Rs. $20$in the $50$ notes.

Note: Here, we have assumed the number of notes of Rs. $10$ be x. You can also solve this question by assuming the number of notes of Rs. $20$ to be x. Then the number of $10$Rs. Notes will become $50 - {\text{x}}$. Follow the same process and you will get the value of x=$30$ which is the number of Rs. $20$ notes. From there you can find the value of notes of Rs. $10$.