Question
A container has a mixture of two liquids, A and B, in
the ratio of 5:3. If 16 liters of the mixture are removed and replaced with 16 liters of liquid B, the ratio of liquids A and B becomes 3:5. Find the initial quantity of liquid A in the container.Solution
ATQ, Let the initial quantity of liquid A be 5x liters and liquid B be 3x liters. After removing 16 liters, 10 liters of A and 6 liters of B are removed. The remaining amounts are: Liquid A: 5x - 10 liters. Liquid B: 3x - 6 liters. After adding 16 liters of liquid B, the new amount of liquid B is 3x + 10 liters. Given the new ratio of A to B is 3:5: (5x - 10) / (3x + 10) = 3 / 5. Cross-multiplying and solving: 25x - 50 = 9x + 30, 16x = 80, so x = 5. Thus, the initial quantity of liquid A is 5 × 5 = 25 liters.
Statements: X @ Y $ Z & U, Z @ V
Conclusions: I. V # X II. V $ X
...Statement: A ≥ B ≥ C = D > E, F > G = H ≤ C
Conclusion: I. C ≥ F II. F > E
...In the question assuming the given statements to be true, find which of the conclusion(s) among given three conclusions is/are definitely follows and t...
Statements: R < S > T; U < V ≤ S; R > P
Conclusions:
I. S > P
II. U < R
III. T < P
Statements: U % X, X & S, S $ J, J # L
Conclusions: I. U & S II. S # L
...Statements: E < S = F < G, H < A ≥ F ≤ B
Conclusion:
I. B > E
II. H ≤ G
Statements: U = R < M < Q < P; A > B > E < R < T; I < N = B > U > X
Conclusions:
I. P ≤ U
II. T > A
...Statements: V = W ≤ X > R ≥ O; C < O; F = X
Conclusion: I. F > R II. X > C
Statements: B > Z > E < X; Z > C > U < F < H; F > S < Y < T
Conclusion:
I. B > Y
II. X < T
...Statement : M=N≥P<Q; R>Q ; T ≥N
Conclusion:
I. N<T
II. N≥R
...
