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.

Solution(By Examveda Team)

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