Question

I have ${\text{Rs1000}}$ in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each domination?

Answer 1

Hint:
let the number of ten rupee notes be $x$ and the number of five rupee notes be $y$
Then $10x + 5y = 1000$ will be our first equation and $y = x + 10$ will be our second equation and hence we can solve and get the values of $x, y$.

Complete step by step solution:
In the question, we are given that ${\text{Rs1000}}$ contains the ten and the five rupee notes and the number of ten rupee notes are ten more than the five rupee notes
So let us suppose that the total number of ten rupee notes be $x$
And the number of five rupee notes be $y$
And we are given that the total amount is ${\text{Rs1000}}$ and as we have $x$ ten rupee notes so the amount made by the ten rupee notes will be ${\text{Rs 10}}x$and the amount made by the five rupee notes will be ${\text{Rs }}5y$ and also we are given that the total amount is ${\text{Rs1000}}$
So we get that $10x + 5y = 1000 - - - - - - - (1)$
Also we are said that the ten rupee notes are ten more than the five rupee notes so we can write that $x = 10 + y$$ - - - - (2)$
Now we have two equations and the two variables so we can easily solve it by using the substitution method.
In the equation (2) we wrote that $x = 10 + y$ so we have the value of $x$ from it
Substituting it in equation (1) we get that
$\Rightarrow 10(y + 10) + 5y = 1000$
$\Rightarrow 10y + 100 + 5y = 1000$
$\Rightarrow 15y = 900$
$\Rightarrow y = 60$
And we know that $x = y + 10$
So putting $y = 60$ in the above equation we get that
$x = 60 + 10 \Rightarrow 70$

So we get that there are $70$ ten rupee notes and $60$ five rupee notes.

Note:
We can also use the single variable to solve this as we can simply suppose that the number of five rupee notes be $x$ so we know that ten rupee notes are ten more so we can say that the ten rupee note will be $x + 10$
Now we can write
$10(x + 10) + 5x = 1000$
And hence we can solve the equation.