Q. There are three mixtures of milk and water named as P, Q, and R. A new mixtures M is formed by mixing 120 ml from mixture P and 96 ml from mixture Q. Now 48 ml mixture from R M in which Milk and water ratio is 2:1 is mixed with 54 ml of mixture M to form new mixture N, such that ratio of milk and water in mixture N becomes 65:37. The ratio of milk and water in mixture P initially is L: K respectively, and in mixture Q is 5:3 respectively. Find the value of [6(L + K) / (2L + K)].
A.7.5
B.3.75
C.3.5
D.4.5
E. None of these
Ans: 3.75
Sol:
54 ml of mixture M mixed with 48 ml of mixture
R, to form mixture N, in which ratio of milk and
water = 65:37
Total milk in mixture N = 65/102 x (54 + 48) = 65
ml
Milk taken from mixture M = 65 – 2/3 x 48 = 33
ml
Total water in mixture N = 37/102 x 102 = 37 ml
Water taken from mixture M = 37 – 1/3 x 48 = 21
Ratio of milk and water in mixture M = 33:21 =
11:7
Total quantity of mixture M = 120 + 96 = 216 ml
Amount of milk in mixture M = 11/18 x 216 = 132
ml
Amount of water in Mixture M = 216 – 132 = 84
ml
Amount of milk taken from P = 132 – 5/8 x 96 =
72 ml
Amount of water taken from P = 84 – 3/8 x 96 =
48 ml
Ratio of milk and water in P = 72:48 = 3:2
Required value = [6 x (3 + 2) / (2 x 3 + 2)] = 3.75
Hence answer is option B