Vessel A contains 30 litres of milk and water in the ratio of 4: 1 and ______litres of mixture is taken out. Then ________litres of the milk are added to the remaining mixture and now the ratio of milk to water becomes is 5: 1.
Q.Which of the following options satisfies the two blanks in the question?
a) 2.5, 5
b) 5, 5
c) 10, 4
d) 5, 6
A. All A, B, C and D
B. Only B and C
C. Only C
D. Only B, C and D
E. Only B
Sol:
From option (A)
Milk in 30 litres the mixture = 30 * 4/5 = 24
Water in 30 litres mixture = 30 * 1/5 = 6
Milk in 2.5 litres the mixture = 2.5 * 4/5 = 2
Water in 2.5 litres the mixture = 2.5 * 1/5 = 0.5
(24 – 2 + x)/ (6 – 0.5) = 5/1
(22 + x)/5.5 = 5/1
22 + x = 27.5
x = 5.5 litres
This will not satisfy the given condition.
From option (B)
Milk in 30 litres the mixture = 30 * 4/5 = 24
Water in 30 litres mixture = 30 * 1/5 = 6
Milk in 5 litres the mixture = 5 * 4/5 = 4
Water in 5 litresthe mixture = 5 * 1/5 = 1
(24 – 4 + x)/ (6 – 1) = 5/1
(20 + x)/5 = 5/1
20 + x = 25
x = 5 litres
This will satisfy the given condition.
From option (C)
Milk in 30 litres the mixture = 30 * 4/5 = 24
Water in 30 litres mixture = 30 * 1/5 = 6
Milk in 10 litres the mixture = 10 * 4/5 = 8
Water in 10 litres the mixture = 10 * 1/5 = 2
(24 – 8 + x)/(6 – 2) = 5/1
(16 + x)/4 = 5/1
16 + x = 20
x = 4 litres
This will satisfy the given condition.
From option (D)
Milk in 30 litres the mixture = 30 * 4/5 = 24
Water in 30 litres mixture = 30 * 1/5 = 6
Milk in 4.5 litres the mixture = 4.5 * 4/5 = 3.6
Water in 4.5 litres the mixture = 4.5 * 1/5 = 0.9
(24 – 3.6 + x)/ (6 – 0.9) = 5/1
(20.4 + x)/5.1 = 5/1
20.4 + x = 25.5
x = 5.1 litres
This will not satisfy the given condition.
