The given question is followed by two statements; select the most appropriate option that solves the question.
Capacity of a solution tank A is 70% of the capacity of tank B. How many gallons of solution are in tank A and tank B?
Statements:
I. Tank A is 80% full and tank B is 40% full.
II. Tank A if full contains 14,000 gallons of solution.
A. Statement I alone is sufficient.
B. Statement II alone is sufficient.
C. Either statement I or II alone is sufficient.
D. Both the statements I and II together are sufficient.
GATE 2015 · General Aptitude · Percentage · medium
Answer: Both statements I and II together are sufficient. Answer: D.
Test Statement I alone: Statement I says A is 80% full and B is 40% full. Volume_A = 0.8 * Capacity_A and Volume_B = 0.4 * Capacity_B. We also know Capacity_A = 0.7 * Capacity_B, so Volume_A = 0.8 * 0.7 * Capacity_B = 0.56 * Capacity_B and Volume_B = 0.4 * Capacity_B. But Capacity_B is unknown. Statement I alone is NOT sufficient.
Test Statement II alone: Statement II gives Capacity_A = 14,000 gal, so Capacity_B = 14,000 / 0.70 = 20,000 gal. We know capacities but not how full each tank is. Statement II alone is NOT sufficient.
Combine both statements: From II: Capacity_A = 14,000 gal, Capacity_B = 20,000 gal. From I: A is 80% full, B is 40% full. Volume_A = 0.80 * 14,000 = 11,200 gal. Volume_B = 0.40 * 20,000 = 8,000 gal. Total = 19,200 gal. Both statements together are sufficient.