Question

In an envelope there are some ₹ 5 notes and some ₹ 10 notes. Total amount of these notes together is ₹ 350 . Number of $₹5$ notes are less by 10 than twice the number of $₹10$ notes. Then find the number of ₹5 and ₹10 notes.

Answer 1

Let the number of $₹5$ notes be ' $x$ ' and the number of $₹10$ notes be ' $y$ '
Total amount of $x$ notes of $₹5=₹5x$
Total amount ofy notes of $₹10=₹10y$
$\therefore$ Total amount $=5x+10y$
According to the first condition,
total amount of the notes together is ₹350.
$\therefore 5x+10y=350$
According to the second condition,
Number of $₹5$ notes are less by 10 than twice the number of $₹10$ notes.
$\therefore x=2y-10$
$\therefore x-2y=-10\dots$. (ii)
Multiplying equation (ii) by 5 ,
$$5x-10y=-50\text{... (iii)}$$
Adding equations (i) and (iii),
$$\begin{array}{cc}& 5x+10y=350\\ & +5x-10y=-50\\ & 10x=300\\ & \therefore x=\frac{300}{10}\\ & \therefore x=30\end{array}$$
Substituting $x=30$ in equation (ii),
$$\begin{array}{cc}& x-2y=-10\\ & 30-2y=-10\\ & \therefore 30+10=2y\\ & \therefore 40=2y\\ & \therefore y=\frac{40}{2}\\ & \therefore y=20\end{array}$$
There are 30 notes of $₹5$ and 20 notes of $₹10$ in the envelope.