Question

Seeta Devi has Rs.9 in fifty paise and twenty-five 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: In this question, we have to find the number of denominations of twenty-five paise and fifty paise coins if the total amount is Rs.9. For this, we will first suppose their denomination as x and y. Then we will calculate the money in terms of variables x and y and equate it to Rs.9. Then we will use another given statement to form one more equation in terms of x and y. Solving the formed equation will give us values of x and y which is our required answer.

Complete step-by-step solution:
Here, Seeta Devi has a denomination of fifty paise and twenty-five paise coins. We have to find the number of denominations if two statements are given.
Let us suppose that she has x number of coins of 50 paise and y number of coins of 25 paise.
We are given that, total money is Rs.9 so let us find money in terms of x and y.
Since the number of 50 paise coins is x, so we can write paise into rupees as:
1 rupee = 100 paise.
50 paise $\dfrac{50}{100}$ rupees = 0.5 rupees.
So money by 50 paise coins will be Rs.0.5x
The number of 25 paise coins is y. Let us convert paise into rupees, we have 100 paise = 1 rupee.
25 paise $\dfrac{25}{100}$ rupees = 0.25 rupees.
So money by 25 paise coins will be Rs.0.25y. So total money will be $Rs.\left( 0.5x+0.25y \right)$.
Since total money is given as Rs.9, so let us equate it.
$0.5x+0.25y=9\cdots \cdots \cdots \left( 1 \right)$.
We are also given that, the number of 25 paise coins is twice that of 50 paise coins. So, we can say that,
$y=2x\cdots \cdots \cdots \left( 2 \right)$.
Putting values of y from (2) into the equation (1) we get:
$0.5x+0.25\left( 2x \right)=9\Rightarrow 0.5x+0.5x=9$
We know $0.5+0.5=1$ so we get: x = 9.
Hence, the number of 50 paise coins is 9 and the number of 25 paise coins is $2\times 9=18$.

Note: Students should note that the money is given in rupees, so to equate it equal to found money, we want our found money in rupees too. Take care while solving decimal numbers and take care of signs while solving equations.