Question

Meena went to a bank to withdraw$2000Rs.$. She asked the cashier to give her 50 rupee and 100 rupee notes only. Meena got 25 notes in all. Find how many notes of 50 rupee and 100 rupee she received.

Answer 1

Hint: First of all we will assume that there might be ‘x’ and ‘y’ be the number of 50 rupee and 100 rupee notes respectively. Then according to the question there are a total 25 notes from which we will get a linear equation in two variables and the sum of the total amount is$2000Rs.$which will give us a second equation. So from these two equations with the help of the substitution method we will get the value of ‘x’ and ‘y’ which are the value of the number of 50 and 100 rupee notes.

Complete step by step answer:
Moving ahead with the question in step-wise manner;
Let us first assume that there is an ‘x’ number of 50 rupee notes.
And ‘y’ number of 100 rupee note.
According to question, as we know that;
Total amount Meena withdraw$=2000Rs.$
Which means sum of total rupee is$2000Rs.$i.e. sum of total amount taken in 50 and 100 rupee note is$2000Rs.$So amount Meena withdraw in the form of 50 rupee note will be 50 multiplied by the number of notes withdraw in the form of 50 rupees. i.e.
Amount withdraw in the form of 50 rupees$=50\times \left( x \right)=50x$
Similarly amount withdrawn in the form 100 rupee note$=100\times \left( y \right)=100y$
So as we know that sum of total amount is$2000Rs.$So we can write it as;
$50x+100y=2000Rs.$ Equation (i)
According to the question we also know that the sum of the total number of notes is 25, i.e. the sum of the number of 50 and 100 rupee notes is 25. So we can write it as;
$x+y=25$ Equation (ii)
Now we have two equation and two variables, so by using the method of substitution we can get the values of ‘x’ and ‘y’. so by applying substitution in Equation (i) and (ii), we will get;
$\begin{align}
  & x+y=25 \\
 & x=25-y \\
\end{align}$
From here put the value of ‘x’ in equation (i), so we will get;
$50\left( 25-y \right)+100y=2000Rs.$
On simplifying it further, we will get;
$\begin{align}
  & 1250-50y+100y=2000Rs. \\
 & 50y=2000-1250 \\
 & 50y=750 \\
 & y=\dfrac{750}{50} \\
 & y=15 \\
\end{align}$
So we got$y=15$, and as ‘y’ is the number of 100 rupee notes, we can say that there are 15 notes of 100 rupee.
Now put the value of ‘y’ in equation (ii) to get the value of ‘x’, so we will get;
$\begin{align}
  & x+y=25 \\
 & x+15=25 \\
 & x=10 \\
\end{align}$
$x=10$
So we got$x=10$, and as ‘x’ is the number of 50 rupee notes, we can say that there are 10 notes of 50 rupee.
Hence answer is 10 and 15, i.e. there are 10 and 15 notes of 50 rupee and 100 rupee which Meena received from the bank.

Note: For the type of question, we always had to assume the unknown quantity some variable (as we did in assuming the number of notes as ‘x’ and ‘y’), which on further solving the problem give us linear equation in two variable which we can solve through substitution method to find out the values of variables.