Question

70 coins of 10 paise and 50 paise are mixed in a purse. If the total value of the money in the purse is Rs. 19, find the number of each type of coin in the purse.

A. Number of 10 paise coins are 60
     Number of 50 paise coins are 20

B. Number of 10 paise coins are 20
    Number of 50 paise coins are 40

C. Number of 10 paise coins are 40
    Number of 50 paise coins are 30

D. Number of 10 paise coins are 30
    Number of 50 paise coins are 50

Answer 1

Hint: In the above equation we will assume the number of 10 paise coins and 50 paise coins as variable. Also we will use the conversion of paise to rupees which is shown below:
100 paise = 1 Rs.

Complete step-by-step answer:
In the above equation we have been given that 70 coins of 10 paise and 50 paise are mixed and the total value of the money is Rs. 19.

Let the number of 10 paise coins be x.

Let the number of 50 paise coins be y.

\[\begin{align}

  & x+y=70 \\

 & \Rightarrow x=70-y.....(1) \\

\end{align}\]

Now the total value of money is Rs. 19 = 1900 paise.

\[\Rightarrow 10x+50y=1900\]

Here, we will use the equation (1) by substituting the value of x, we get:

\[\begin{align}

  & 10(70-y)+50y=1900 \\

 & 700-10y+50y=1900 \\

 & 40y=1900-700 \\

 & 40y=1200 \\

 & y=\dfrac{1200}{40}=30 \\

 & \Rightarrow y=30 \\

\end{align}\]

And we have \[x=70-y\]

\[\begin{align}

  & x=70-39=40 \\

 & \Rightarrow x=40 \\

\end{align}\]

Hence there are 30 fifty paise coins and 40 ten paise coins in the purse.

Therefore, the correct option of the above equation is option C.


Note: Just be careful while doing calculation as there is a chance that you might make a mistake and get an incorrect answer.