Question

A bag contains Rs.90 in coins. If coins of 50 paise, 25 paise and10 paise are in the ratio 2:3:5, the number of 25 paise coins in the bag is
A. 80
B. 100
C. 120
D. 135

Answer 1

Hint: First we assume that the number of 50 paise , 25 paise and 10 paise coins be 2x , 3x and 5x respectively. After this we will multiply 2x by $\dfrac{1}{2}$ , 3x by $\dfrac{1}{4}$ and 5x by $\dfrac{1}{{10}}$. Finally add them and equate them to 90 to get the equation.

Complete step-by-step answer:

Total value of coins = Rs. 90.

Number of 50 paise coins : Number of 25 paise coins : number of 10 paise coins =2:3:5.
Let the number of 50 paise , 25 paise and 10 paise coins be 2x , 3x and 5x respectively.
We know that :

50 paise = Rs.$\dfrac{1}{2}$

25 paise = Rs.$\dfrac{1}{4}$

10 paise = Rs. $\dfrac{1}{{10}}$.

$\therefore $ Value of 50 paise coins in rupees = Rs.2x$ \times \dfrac{1}{2}$ = Rs. x

      Value of 25 paise coins in rupees= Rs. 3x$ \times \dfrac{1}{4} =

{\text{Rs}}{\text{.}}\dfrac{{3{\text{x}}}}{4}$

     Value of 25 paise coins in rupees = Rs. 5x$ \times \dfrac{1}{{10}} =

{\text{Rs}}{\text{.}}\dfrac{{\text{x}}}{2}$ .


Total value of coins = Rs.(x+$\dfrac{{3{\text{x}}}}{4} + \dfrac{{\text{x}}}{2}$ )=

Rs.$\dfrac{{9{\text{x}}}}{4}$.

According to question:

$

  \dfrac{{9{\text{x}}}}{4} = 90 \\

   \Rightarrow {\text{x = }}\dfrac{{90 \times 4}}{9} = 40 \\

 $

Therefore, we can say that:

Number of 50 paise coins = 2$ \times $40 = 80.

Number of 25 paise coins = 3$ \times $40 = 120.

Number of 50 paise coins = 5$ \times $40 = 200.

$\therefore $ Number of 25 paise coins = 120.

Therefore, option C is correct.


Note: If the ratio of the quantities are given then the real quantities are obtained by multiplying the individual numbers in the ratio by their common factor. For example if three numbers in ratio are a:b:c the assuming that their common factor is ‘x’, we can write the first number as ‘ax’ , second number as ‘bx’ and third number as ‘cx’. In this question, you have to convert the numbers into their respective value in rupees because the total amount is given in rupees.