two containers A and B contain mix of water and milk in the ratio of 5:2 and 7:6 respectively find the ratio in which these two mixtures can be mixed so that a new mixture formed in the container C in the ratio of 8:5
A 2:7
B 7:9
C 9:7
D 5:7
Answers
Answer:
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Step-by-step explanation:
Two containers A and B mix of water and milk in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these two mixtures can be mixed so that a new mixture form in the container with ratio of 8 : 5?
Let a and b be the amount of mixture taken from A and B respectively and poured to container C.
Amount of water in C = (5a/(5+2))+ (7b/(7+6)) = (5a/7)+(7b/13)
Amount of milk in C = (2a/(5+2))+ (6b/(7+6)) = (2a/7)+(6b/13)
Target ratio of water and milk = 8/5
[(5a/7)+(7b/13)]/ [(2a/7)+(6b/13)] = 8/5
By simplification,
a/b = 7/9
Ans: Ratio = 7:9
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Two mixtures of ratio 5 :2 and 7 : 6 must be mixed in 7 : 9 ratio to get final mixture 8 : 5
Given : Two containers A and B contain mix of water and milk in the ratio of 5:2 and 7:6 respectively
To Find :Ratio in which these two mixtures can be mixed so that a new mixture formed in the container C in the ratio of 8:5
Solution:
Let say solutions A and B are mixed in m : n ratio
Container A Water : Milk = 5 : 2
Water = 5m/7
Milk = 2m/7
Container B Water : Milk = 7 : 6
Water =7n/13
Milk = 6n/13
Water = 5m/7 + 7n/13
= ( 65m + 49n)/91
Milk = 2m/7 + 6n/13
= (26m + 42n)/91
Rati = 8 : 5
=> ( 65m + 49n) / (26m + 42n) = 8/5
=> 325m + 245n = 208m + 336n
=> 117m = 91n
=> 9m = 7n
=> m/n = 7/9
=> m : n = 7 : 9
correct option is B 7:9
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