Question

Sirisha has Rs.9 in fifty – paisa and twenty paise coins. She has twice as many twenty five paise coins as she has fifty paise coins. How many coins of each kind does she have?

Answer 1

Hint: Assume that Sirisha has ‘x’ 50 paise coin and ‘y’ 25 paise coin. Convert Rs.9 into paise by using the relation: - 1Rs. = 100 paise. Now, form two linear equations in two variables x and y using the given information. Solve the two equations to find the value of x and y and get the answer.

Complete step-by-step answer:
Here, we have been given that Sirisha has a total of Rs.9 which is a combination of a certain number of 50 paise coins and 25 paise coins. We have to find that number.
Let us assume the number of 50 paise coins and 25 paise coins that Sirisha has is x and y respectively. Now, we know that: - 1Rs. = 100 paise, so she has: -
\[\Rightarrow \] 9Rs. = 9 \[\times \] 100 paise
\[\Rightarrow \] 9Rs. = 900 paise
Therefore, Sirisha has 900 paise. So, the sum of these x 50 paise coins and y 25 paise coins will be 900. So, we have,
\[\Rightarrow 50x+25y=900\]
\[\Rightarrow 2x+y=36\] - (1)
Now, we have been provided with the information that she has twice as many twenty - five paise coins as she has fifty paise coins. So, according to the question we have,
\[\Rightarrow y=2x\] - (2)
Substituting the value of y from equation (2) in equation (1), we get,
\[\begin{align}
  & \Rightarrow 2x+2x=36 \\
 & \Rightarrow 4x=36 \\
 & \Rightarrow x=9 \\
\end{align}\]
Substituting x = 9 in equation (2), we get,
\[\begin{align}
  & \Rightarrow y=2\times 9 \\
 & \Rightarrow y=18 \\
\end{align}\]
Hence, Sirisha has a total of ‘9’ 50 – paise coins and ‘18’ 25 – paise coins.

Note: One may note that here we have assumed two variables x and y because we had to find two things, number of 50 paise coins and number of 25 paise coins. Here, we have converted Rs.9 into paise by multiplying it with 100. We can also solve the question by converting paise into rupees by dividing the assumed paise by 100. So, the relation would have been one 50 paise = \[\dfrac{1}{2}\]Rs. And one 25 paise = \[\dfrac{1}{4}\]Rs.