A jar contains 35% syrup in the mixture of syrup and water. A part of this mixture is replaced by another mixture containing 20% syrup. Now, in the new mixture, the percentage of syrup is found to be 24%. What is the ratio in which these mixtures were mixed to obtain the new mixture?

Explanation

∴ The ratio of mixtures is 4 : 11. Alternate Method Concept Used: Use the concept of weighted average to determine the ratio in which the mixtures were combined. Formula Used: Weighted average formula: Final percentage = a×percentage of mixture A+b×percentage a+b of mixture B ​ Calculation: Mixture A (original): 35% syrup Mixture B (replacement): 20% syrup Final mixture: 24% syrup Using the weighted average formula: 0.35 × (1 − x) + 0.20 × x = 0.24 0.35 - 0.35x + 0.20x = 0.24 0.35 - 0.15x = 0.24 0.15x = 0.35 - 0.24 0.15x = 0.11 x = 0.11 0.15 ​x = 11 15 ​ The fraction of Mixture A replaced is 1115111511151115 . The fraction of Mixture A remaining is 1 −1115 =4151 −1115 =4151 −1115 =4151−1115=415 . Therefore, the ratio of Mixture A to Mixture B is 415 :1115415 :1115415 :1115415:1115 or 4 : 114 : 114 : 114:11 . So, the ratio in which these mixtures were mixed to obtain the new mixture is 4:11.