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Let A be closed after x minutes. Then, Part filled by (A + B) in x min. + part filled by B in (12 – x) min. = 1 x (1/12 + 1/16 ) + (12 – x ) × 1/16 = 1 ⟹ (7 x)/48 + (12 - x)/16 = 1 ⟹ (7 x)/48 + 3/4 - x/16 = 1 ⟹ (4 x)/48 = 1/4 ∴ x = 3 ∴ Hence, A must be closed after 3 minutes.
1 6 13 24 41 ?
35 36 68 207 836 4205
...Select the number from among the given options that can replace the question mark (?) in the following series.
2, 6, 12, 20, ?, ?
56, 57, 49, 76, 12, ?
8 9 22 75 316 ?
...1331 1000 729 512 ? 216
...8 9 22 75 316 ?
...19, 37, 65, 91, 127, 169
9, 21, 67, 273, 1371, ?
40 30 20 ? 7.5 4.375