A bag has coins of 50 paisa, 25 paisa and 10 paisa in the respective ratio of 5 : 8 : 3 whose total value is Rs.144. Find the number of 50 paisa coins.

Answer: Option D

Ratio of the number of 50 paisa, 25 paisa and 10 paisa coins = 5 : 8 : 3
Ratio of their values
$$\begin{array}{rl}& =\frac{5}{8}:\frac{8}{4}:\frac{3}{10}\\ & \text{LCM of 2, 4 and 10}=20\\ & =\left(\frac{5}{2}\times 20\right):\left(\frac{8}{4}\times 20\right):\left(\frac{3}{10}\times 20\right)\\ & =50:40:6\\ & \text{Sum of the terms of ratio}\\ & =50+40+6=96\\ & \therefore \text{Value of 50 paisa coins}\\ & =\frac{50}{96}\times 144=75\\ & \therefore \text{Number of 50 paisa coins}\\ & =75\times 2=150\end{array}$$