Question

In a cash bag, there are a total of fifty six 25paise and one rupee coins. If the total amount in the form of 25paise and one rupee coins is Rs.35, how many 25paise coins are there in the bag?
A). 20
B). 28
C). 42
D). 56

Answer 1

Hint: We are given a total number of 56 coins of 25paise and one rupee in a cash bag. We will let the number of 25paise coins be \[x\] then, the number of one rupee coins will be \[56 - x\]. And further we are told that the amount in total is Rs.35. So now, we will add the individual amount of 25paise coins and one rupee coins equating them to Rs.35 to form an equation. And at the end we will solve for \[x\] to get the number of 25paise coins in the cash bag.

Complete step-by-step solution:
 Given, Total number of 25paise and one rupee coins = 56
Let us assume that the number of 25paise coins in a bag =\[x\]
Then, the number of one rupee coins in a bag = \[56 - x\]
Total amount in the form of 25paise coins and one rupee coins = Rs.35
Amount in the form of 25paise coins = \[\dfrac{{25}}{{100}}x\] [because, 1 rupee = 100paise]
Amount in the form of one rupee coins = \[56 - x\]
Then, \[\dfrac{{25}}{{100}}x + \left( {56 - x} \right) = 35\]
Simplifying the above equation,
\[
  \dfrac{x}{4} - x = 35 - 56 \\
   \Rightarrow - \dfrac{3}{4}x = - 21 \\
 \]
Finally, we get,
\[x = 28\]
There are 28 coins of 25paise in the bag.

Note: Alternatively, this question can also be done using two variables.
We will let the number of 25paise coins as \[x\] and number of one rupee coins as \[y\]. One equation can be formed using these two variables simply by adding them and equating to the total number of coins. And further we are told that the amount in total is Rs.35. So now, we will add the individual amount of 25paise coins and one rupee coins equating them to Rs.35 to form another equation. Now, we have two linear equations having two variables. We will solve them now using either a substitution method or elimination method.