A bag has Rs. 51.25 in the form of 2-rupee, 50-paise and 25-paise coins in the ratio of 3 : 5 : 7. What is the total number of 50-paise coins?

Solution(By Examveda Team)

\[\begin{array}{*{20}{c}} {}&{{\text{Rs}}{\text{. 2}}}&{}&{{\text{50 Paise }}}&{}&{{\text{25 Paise}}} \\ {{\text{Coins}}}&3&:&5&:&7 \end{array}\]
Amount = Number of coins × Face value
Amount = $$6:\frac{5}{2}:\frac{7}{4}$$
According to question,
$$\eqalign{ & \Rightarrow 6x + \frac{{5x}}{2} + \frac{{7x}}{4} = 51.25 \cr & \Rightarrow 24x + 10x + 7x = 51.25 \times 4 \cr & \Rightarrow 41x = 205 \cr & \Rightarrow x = \frac{{205}}{{41}} \cr & \boxed{x = 5} \cr} $$
∴ Total number of 50 paise coins = 5 × 5 = 25