Question

A bag contains 25 paise, 10 paise and 5 paise coins in the ratio 1:2:3. If their total value is Rs.30, 5 paise coins are,
(a) 50
(b) 100
(c) 150
(d) 200

Answer 1

Hint: Take ‘6x’ as the number of coins present inside the box. Find the ratio in which 25 paise, 10 paise and 5 paise are arranged and add them together. Equate them to a total value of Rs.30. Find the value of x to get the number of coins of each type.

Complete step-by-step answer:
Given that a bag contains 25 paise, 10 paise and 5 paise coins. Now let us consider the total number of coins present in the box as ‘6x’. The coins 25 paise, 10 paise and 5 paise are in the ratio of 1:2:3. i.e. 25 paise in ratio of 1, 10 paise in ratio of 2 and 5 paise in ratio of 3. So the exact quantities become x, 2x and 3x respectively.

We know 25 paise can be written as \[\dfrac{25}{100}\]or 0.25, and 5paise can be written as \[\dfrac{5}{100}\]or 0.05.
We have been given the total value of money in the box as Rs.30.

The total value of all coins in the box can be combined and written as-
\[5\times \dfrac{25}{100}+x\times \dfrac{2\times 10}{100}+x\times \dfrac{3\times 5}{100}\]or
\[\left( x\times 0.25 \right)+\left( x\times 0.2 \right)+\left( x\times 0.15 \right)=0.6x\]

Thus we can say that the total value of all coins in the box is Rs.30.
\[\begin{align}
  & \therefore 0.6x=30 \\
 & x=\dfrac{30}{0.6}=\dfrac{30\times 10}{6}=\dfrac{300}{6}=50 \\
\end{align}\]

Hence the number of 50 paise coins = x = 50.
10 paise coins = 2x = \[2\times 50\]= 100.

Similarly, 5 paise coins = 3x = \[3\times 50\]= 150.
\[\therefore \]The number of 5 paise coins = 150.
\[\therefore \]Option (c) is the correct answer.

Note: The ratio is given as 1:2:3 and the number of coins is taken as ‘x’. Remember how to find the equation with this content. Making mistakes in how to form the equation will affect the final answer. We got a value of x = 50. But we are asked to find a number of 5 paise coins, whose value is 3x and not just x.