Question

A man has only 20 paise coins and 25 paise coins in his purse. If he has 50 coins in all totaling Rs.11.25. How many coins of each kind does he have?

Answer 1

Hint: Given that the man has two types of coin in his purse.
First we take a variable as the number of 20 paise coins and another for 25 paise coins.
Then applying the two conditions we will get two equations.
By solving the equations we will get the number of 20 paise coins and the number of 20 paise coins in his purse.

Complete step by step answer:
It is given that the man has only 20 paise coins and 25 paise coins in his purse.
Let, the number of 20 paise coins in his purse be x & the number of 25 paise coins in his purse be y
Again it is given that the number of total coins he has is 50.
Thus, \[x + y{\rm{ }} = 50\]
\[y = 50 - x\]…… (1)
Total amount he has $Rs.11.25$
We know that \[1rs = 100paise\]
Let us convert the total amount in paise, then we get
\[ = 11.25 \times 100\]
\[ = 1125paise\]
So he has the total amount for 20 paise coins\[ = 20 \times x\]
That is \[20x\]
Also he has the total amount for 25 paise coins = \[25 \times y\]
That is\[25y\]
So the total amount \[ = 20x + 25y\]
Let us equate the total amount found with the given amount we get,
\[20x + 25y = 1125\]
Divide the above equation by 5 we get,
\[4x + 5y = 225.......(2)\]
Let us substitute the value of y from (1) in (2) we get,
\[4x + 5(50 - x) = 225\]
On simplifying the above equation,
\[4x + 250 - 5x = 225\]
From this equation we get,
\[x = 25\]
Now let us substitute the value of \[x\] in equation (1) we get, \[\;y = 50 - 25 = 25.\]
Therefore, we have found that\[x = 25,y = 25\].

Hence the number of 20 paise & 25 paise coins are 25 & 25 respectively.

Note:
we all know that \[1rs = 100paisa\] we use this term and change the total amount given in paisa because we are given the coins in paisa. If it was retained in rupees it would be far difficult to find the answer.