CAT 2017 Slot 2 — QA Question 14
Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B and C respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has
Answer & solution
- A
The same amount of water and liquid B
- B
The same amount of liquids B and C
More water than liquid B
- D
More water than liquid A
Proportion of water in three mixtures with A, B and C is , and respectively.
[Sum of these proportions is 4, 5 and 6 and LCM(4, 5, 6) = 60]
Now as three mixture with A, B and C are mixed in the ratio 4 : 3 : 2.
Let the amount of three mixtures mixed be 4 × 60, 3 × 60 and 2 × 60 = 240, 180 and 120 liters respectively.
Quantity of water in liquid A, B and C is × 240 + × 180 + × 120 = 80 + 45 + 24 = 149
Quantity of liquid A in resultant mixture = × 240 = 160
Quantity of liquid B in resultant mixture = × 180 = 135
Quantity of liquid C in resultant mixture = × 120 = 96
Now let is examine the options individually
(a) The resultant mixture has 149 liters water and 160 of liquid B.
Hence, option (a) in incorrect.
(b) The resultant mixture has 135 liters of liquid B and 96 liters of liquid C.
Hence, option (b) is incorrect.
(c) Now quantity of water in resultant mixture 149 liters and quantity of liquid B is 135 liters.
Hence, option (c) is correct.
(d) Quantity of liquid A in resultant, mixture is 160 liters and quantity of water = 149 liters.
Hence, option (d) is incorrect.
Hence, option (c).