Six coins of gold and silver of equal weights are melted and new coins are cast. The ratio of gold and silver in one of the coins is 2 : 1, in another two coins 3 : 5 and 7 : 5 in the remaining coins. What will be the ratio between gold and silver respectively in the new coins ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Gold in new coins}} \cr & = \left( {\frac{2}{3} + 2 \times \frac{3}{8} + 3 \times \frac{7}{{12}}} \right){\text{units}} \cr & = \left( {\frac{2}{3} + \frac{3}{4} + \frac{7}{4}} \right){\text{units}} \cr & = \frac{{19}}{6}{\text{units}}{\text{}} \cr & {\text{Silver in new coins}} \cr & = \left( {\frac{1}{3} + 2 \times \frac{5}{8} + 3 \times \frac{5}{{12}}} \right){\text{units}} \cr & = \left( {\frac{1}{3} + \frac{5}{4} + \frac{5}{4}} \right){\text{units}} \cr & = \frac{{17}}{6}{\text{units}}{\text{.}} \cr & \therefore {\text{Required ratio}} \cr & = \frac{{19}}{6}:\frac{{17}}{6} \cr & = 19:17 \cr} $$