Let Q be closed after x minutes. Then, Part filled by (P+Q) in x min. + part filled by P in (36 – x ) min. = 1 x(1/48 + 1/64) + (36 - x) x 1/48 = 1 ⟹(7x/192) + (36 - x)/48 = 1 ⟹ 7x + 4 (36 –x ) = 192 ∴ x = 16 ∴ Hence, Q must be closed after 16 minutes
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