There are Rs. 225 consisting of one rupee, 50 paise and 25 paise coins. The ratio of their numbers in that order is 8 : 5 : 3. The number of one - rupee coins is = ?

Solution(By Examveda Team)

Rs. 1 : 50 paise : 25 paise
Number of coins 8x : 5x : 3x
$$\eqalign{ & {\text{Value of coins}} \cr & {\text{ = }}\frac{{8x}}{1}:\frac{{5x}}{2}:\frac{{3x}}{4} \cr & \therefore 8x + \frac{{5x}}{2} + \frac{{3x}}{4} = {\text{Rs}}.\,225, \cr & {\text{Given}}\frac{{32x + 10x + 3x}}{4} = 225 \cr & \Rightarrow 45x = 225 \times 4 \cr & \Rightarrow x = \frac{{225 \times 4}}{{45}} \cr & \Rightarrow x = 5 \times 4 = 20 \cr} $$
∴ Number of one rupees coins
= 20 × 8 = 160