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The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. In how much time will pipe A alone fill the tank? I) When pipes A & B are simultaneously opened and closed after 5 and 3 hours respectively, the tank is only 7/12 filled. II) Pipe B can alone fill the tank in 12 hours. III) When pipes A & B are simultaneously opened and closed after 3 and 4 hours respectively, the tank is only 8/15 filled.

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. In how much time will pipe A alone fill the tank? I) When pipes A & B are simultaneously opened and closed after 5 and 3 hours respectively, the tank is only 7/12 filled. II) Pipe B can alone fill the tank in 12 hours. III) When pipes A & B are simultaneously opened and closed after 3 and 4 hours respectively, the tank is only 8/15 filled. Correct Answer Any two

Let part filled by pipes A & B in 1 hr. be ‘A’ and ‘B’ respectively

Considering statement I,

⇒ 5A + 3B = 7/12      ----(1)

Considering statement II,

⇒ B = 1/12      ----(2)

Considering statement III,

⇒ 3A + 4B = 8/15      ----(3)

Considering statements I and II,

Substituting (2) in (1),

⇒ 5A = 7/12 - 1/4 = 1/3

⇒ A = 1/15

⇒ Pipe A will fill the tank alone in 15 hours

Considering statements I and III,

Multiplying (1) by 4 and (3) by 3 and equating,

⇒ 4(5A + 3B - 7/12) = 3(3A + 4B - 8/15)

⇒ 20A + 12B - 7/3 = 9A + 12B - 8/5

⇒ 11A = 11/15

⇒ A = 1/15

⇒ Pipe A will fill the tank alone in 15 hours

Considering statements II and III,

Substituting (2) in (3),

⇒ 3A = 8/15 - 1/3 = 1/5

⇒ A = 1/15

⇒ Pipe A will fill the tank alone in 15 hours

∴ The question cam be answered using any two of the given statements

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