Question

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

Answer 1

Hint: Consider the number of Rs. 50 and Rs. 100 notes as x and y. Find an equation with the number of notes. Similarly, find an expression relating to notes and the total amount. Solve these 2 expressions to find x and y.

Complete step-by-step answer:
Let us consider the number of Rs. 50 notes to be ‘x’ and the number of Rs. 10 notes to be ‘y’.
She got the total number of notes as 25.
So, number of 50 rupees notes + number of 100 rupees notes = 25.
\[\therefore x+y=25.......(1)\]
We are given the total amount that Meena withdrew = Rs. 2000.
If number of Rs. 50 notes is 1 and number of Rs. 100 notes is 1, then the total amount becomes \[50\times 1+100\times 1=150.\]
Similarly, if we take 2 notes of Rs. 50 and 3 notes of Rs. 100, then total amount becomes \[50\times 2+100\times 3=400.\]
So let’s take ‘x’ notes of Rs. 50 and ‘y’ notes of Rs. 100. Then total amount becomes \[50x+100y.\]
We know, (money withdrawn with Rs. 50 note) + (money withdrawn with Rs. 100 note) = Rs. 2000.
\[50\times \](number of Rs. 50 notes) \[+100\times \](number of Rs. 100 notes) = 2000.
\[\begin{align}
  & \Rightarrow 50x+100y=2000 \\
 & x+2y=\dfrac{2000}{50} \\
 & x+2y=40........(2) \\
\end{align}\]
Now let us solve equation (1)and (2) by method of substitution.
From equation (1), \[x=25-y\], substitute this value in equation (1).
\[\begin{align}
  & 25-y+2y=40 \\
 & 25 +y=40 \\
 & \therefore y=40-25=15 \\
\end{align}\]
Number of Rs. 100 note = y =15.
So number of Rs. 50 note,
\[\begin{align}
  & x=25-y \\
 & x=25-15 \\
 & \therefore x=10 \\
\end{align}\]
So the number of Rs. 50 notes withdrawn is 10 and the number of Rs. 100 notes are 15.

Note: The two expressions can be solved by adding or subtracting for elimination of one variable.
\[x+y=25\] and \[x+2y=40\]
Let us write these expressions as,
\[\begin{align}
  & x+y=25 \\
 & x+2y=40 \\
\end{align}\]
Subtract them and cancel the like terms.
\[\begin{align}
  & x+y=25 \\
 & x+2y=40 \\
 & \_\_\_\_\_\_\_\_\_\_ \\
 & 0-y=-15 \\
\end{align}\]
Hence we got
 \[\begin{align}
  & -y=-15 \\
 & \Rightarrow y=15. \\
\end{align}\]
Similarly
 \[\begin{align}
  & x+y=25 \\
 & x+15=25 \\
 & \therefore x=10. \\
\end{align}\]