Question

A bag contains 25 paise and 50 paisa coins whose total value is Rs.30. if the number of 25 Paise coins is four times that of 50 paise coins, find the number of each type of coins.

Answer 1

Hint: Consider 25 paise coins as x, 50 paisa coins as y. Now for an equation based on the facts given in the question and then solve them simultaneously.

Complete Step-by-Step solution:
In the question, a bag is given which contains 25 paise and 50 paisa coins whose total value is ₹ 30. We are further informed that the number of 25 paise coins is four times than that of 50 paise coins.
The total amount is given ₹30. First of all we will change ₹30 into paisa by using the fact that ₹1 is 100 paisa, so ₹30 is 3000 paisa.
So, the total amount is 3000 paisa which is available in form of 25 paise and 50 paisa coins.
Let’s consider the number of coins of 25 paisa be x and number of coins of 50 paisa be y in the bag.
So, the amount bag contain in term of x and y be,
 $25\times x+50\times y=25x+50y$
The amount in the bag in paisa is 3000. So, we can say that,
$25x+50y=3000$
This can be further simplified by dividing 25 throughout so, we get
$x+2y=120\ldots \left( i \right)$
In the 2nd line of the question it is written that the number of 25 paise coins is four times the number of 50 paise coins. So, we can write it as,
$x=4y\ldots \left( ii \right)$
Now we will use the equation (ii) and substitute in equation (i) so, we get
$\begin{align}
  & 4y+2y=120 \\
 & \Rightarrow 6y=120 \\
 & \Rightarrow y=\dfrac{120}{6}=20 \\
\end{align}$
Now as we know, y=20. So,
$\begin{align}
  & x=4y \\
 & \Rightarrow x=4(20)=80 \\
\end{align}$
So, the number of 25 paise coins is 80 and the number of 50 paise coins is 20.

Note: Instead of forming two equations one can consider the number of 50 paise coins is x so, the number of 25 paise coins will be 4x.