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?

Answer: Option C

\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,
$$\begin{array}{rl}& \Rightarrow 6x+\frac{5x}{2}+\frac{7x}{4}=51.25\\ & \Rightarrow 24x+10x+7x=51.25\times 4\\ & \Rightarrow 41x=205\\ & \Rightarrow x=\frac{205}{41}\\ & \boxed{x=5}\end{array}$$
∴ Total number of 50 paise coins = 5 × 5 = 25