Question

A bag contains Rs 750 in the form of rupee, 50 P and 25 P coins in the ratio 5:8:4. Find the number of coins of each type.

Answer 1

Hint: It is given in the question that number of rupee, 50 P and 25 P coins are in the ratio 5:8:4 so from ratio concept we can convert the ratio into number by multiplying each ratio with x we get the number of rupee coins as 5x, number of 50 P coins as 8x and 25 P coins as 4x. Now, it is given that the total amount of money in the bag is Rs 750 so add all the denomination of coins and equate it to 750. From there you will get the value of x and hence will get the number of coins of each denomination.

Complete step-by-step answer:
The amount of money a bag contains is Rs 750. It is given that inside the bag the coins of rupee, 50 P and 25 P are in the ratio of 5:8:4. To get the number of coins of each denomination we will multiply the ratio by x. After multiplying the ratio by x we get,
Number of rupee coins $=5x$
Number of 50 P coins $=8x$
Number of 25 P coins $=4x$
The value in rupees corresponding to 5x number of rupee coins is equal to:
$5x\left( 1 \right)=\text{Rs }5x$
Using the conversion Re. 1 = 100 paise, the value in rupees corresponding to 8x number of 50 P coins is equal to:
$\begin{align}
  & 8x\left( \dfrac{50}{100} \right) \\
 & =8x\left( \dfrac{1}{2} \right)=4x \\
\end{align}$
Using the conversion Re. 1 = 100 paise, the value in rupees corresponding to 4x number of 25 P coins is equal to:
$4x\left( \dfrac{25}{100} \right)$
$=4x\left( \dfrac{1}{4} \right)=x$
Now, the total sum of money in the bag is Rs 750 so adding the amount of money with different denominations and equating to 750 we get,
$\begin{align}
  & 5x+4x+x=750 \\
 & \Rightarrow 10x=750 \\
\end{align}$
Dividing 10 on both the sides of the above equation we get,
$x=75$
Now, substituting the above value of x in 5x, 8x and 4x we get,
Number of rupee coins $=5\left( 75 \right)=375$
Number of 50 P coins $=8\left( 75 \right)=600$
Number of 25 P coins $=4\left( 75 \right)=300$
In the above equations, we have found the number of rupee, 50 P and 25 P coins.

Note: You can verify the number of coins of different denominations that you are getting is correct by multiplying the number of coins with their corresponding value and then add the value of the three denominations of coins in the bag and then see whether their sum is equal to 750 or not.
$\begin{align}
  & 375\left( 1 \right)+600\left( \dfrac{1}{2} \right)+300\left( \dfrac{1}{4} \right) \\
 & =375+300+75 \\
 & =750 \\
\end{align}$
From the above calculations, we have determined that the sum of the different denominations of the coins is equal to the amount of money in the bag which is equal to Rs 750.