Question

An amount of Rs.$27$ is in the form of $50$ paise, $25$ paise and $20$ paise. The number $25$paise coins is doubled the number of $20$ paise coins but half the number of $50$ paise coins. Find the number of coins of $50$ paise.

Answer 1

Hint: We are given a certain amount of money in the form of $50$paise, $25$paise and $20$paise coins. We are given the coins number. We have to find the number of coins of each type given we will assume the number of coins of each type equal to some variable example p,q,r respectively and convert Rs into paise.
$1$Rs =$100$paise
We will form the equation and equate it to the amount given and find the value of variables using the substitution and elimination method. Because there will be three variables. We will find the value of one variable in the form of another and substitute it in the other equations. By solving the equations then we will find the value of one variable in the form of another and substitute it in the form of other equations. By solving these we will find the value of variables and then we will get the number of coins of each type.

Complete step-by-step answer:
Step1: We are given the number of $25$paise coins double to that of $20$paise coins and half the number of $50$paise coins.
Let the no of $50$paise coins be $x$, $25$paise coins be $y$and $20$paise coins be $z$respectively.
Adding the amount formed by different coins and equate it equal to Rs$2700$
$ \Rightarrow 50x + 25y + 20z = 2700$............…(1)
$ \Rightarrow y = 2z$..............…(2)
So , $\dfrac{x}{2} = 2z$
Finding the value of $x$
$x = 4z$…(3)
From (1), (2) and (3) substituting the values of $x$ and $y$
$50(4z) + 25(2z) + 20z = 2700$
$ \Rightarrow 200z + 50z + 20z = 2700$
$ \Rightarrow 270z = 2700$
$ \Rightarrow z = 10$
From equation (2) we will find the value of$y$
$ \Rightarrow y = 2z$
Substituting the value of $z = 10$ we get:
$ \Rightarrow y = 2 \times 10$
$y = 20$
From (3) we will substitute the value of $z$and get
$x = 4 \times 10$
$x = 40$
$\therefore $ So , the number of $50$ paise coins$ = x = 40$
 The number of $25$paise coins $ = y = 20$
The number of $20$paise coins $ = z = 10$

The total number of 50 paise coins are 40.

Note: We can also verify whether the answer which we got is correct or wrong.
So we got a total of 40, 50 paise coins which is equal to $40 \times 50$ = $2000$paise = $20$Rs.
20, 25 paise coins which is equal to $20 \times 25$ = $500$paise = $5$Rs.
10, 20 paise coins which is equal to $10 \times 20$ = $200$paise = $2$Rs.
The total sum = $20+5+2$ = $27$ which is equal to the amount given in the question.
So the answer which we got is correct.