A lady went to a bank with a cheque of Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 2000 currency notes in return. She got 125 currency notes in all. Find the number of each kind of currency notes.

Given:

A lady went to a bank with a cheque of Rs. 1,00,000. She asked the cashier to give her Rs. 500 and Rs. 2,000 currency notes in return. She got 125 currency notes in all.

To do: 

We have to find the number of each kind of currency notes she received.

Solution:

Let the number of Rs. 500 notes be $x$ and the number of Rs. 2000 notes be $y$.

The total number of notes $= 125$

This implies,

$x + y = 125$

$x = 125-y$....(i)

Total amount only in Rs. 500 notes $= 500x$

Total amount only in Rs. 2000 notes $=2000y$

Total amount $=Rs.\ 100000$

$500x + 2000y = 100000$

$500(125-y) + 2000y = 100000$    (From (i))

$500\times125 - 500y + 2000y = 100000$

$62500 +1500 y = 100000$

$1500y = 100000-62500 = 37500$

$y = \frac{37500}{1500} = 25$

$ x = 125-25 = 100$    (From (i))

Therefore, she received $100$ Rs. 500 notes and $25$ Rs. 2000 notes.