Question

Savita has Rs.27 in the form of fifty paise and twenty-five paise coins. She has twice as many twenty-five paise coins as she has 50 paise coins. How many coins of each kind does she have?

Answer 1

Hint: Let the number of 50 paise coins be x and the number of 25 paise coins be y. Given that y is twice of x which means y is equal to 2x. And then calculate the total amount formed by 50 paise coins and 25 paise coins in rupees. Add these two amounts and equate it to Rs.27 to find the no. of 25 paise coins and 50 paise coins.

Complete step-by-step answer:
We are given that Savita has Rs.27 in the form of fifty paise and twenty-five paise coins and she has twice as many twenty-five paise coins as she has 50 paise coins.
We have to find the no. of 25 paise and 50 paise coins Savita have.
Let the number of 50-paise coins be x and the number of 25-paise coins be y.
We are given that the no. of 25-paise coins is twice the no. of 50-paise coins.
This means, $ y = 2x $
100 paise is equal to 1 rupee.
50 paise is equal to $ \dfrac{{50}}{{100}} = 0.5 $ rupees and 25 paise is equal to $ \dfrac{{25}}{{100}} = 0.25 $ rupees.
So the amount formed by all the 50 paise coins is $ 0.5x $ rupees and the amount formed by all the 25 paise coins is $ 0.25y = 0.25 \times 2x = 0.5x $ rupees.
The total amount Savita has is Rs.27. This means
 $ \Rightarrow 0.5x + 0.5x = 27 $
 $ \Rightarrow 1x = 27 $
 $ \therefore x = 27 $
Therefore, x which is the no. of 50 paise coins is 27 and the no. of 25 paise coins is $ y = 2x = 2 \times 27 = 54 $
Savita has 27 50-paise coins and 54 25-paise coins.
So, the correct answer is “Savita has 27, 50-paise coins and 54, 25-paise coins”.

Note: As the amount Savita has is given in rupees, we had to convert the amount of coins which are in paise into rupees otherwise the results will be wrong. Paise are converted into rupees by dividing with 100 whereas to convert rupees into paise, we have to multiply by 100 to the number.