2002 · Q44
A factory has three belt conveyors fitted in its loading station. Conveyors 'A' and 'B' operating simultaneously lift all the goods in the same time during which the goods can be lifted by the conveyor 'C' operating alone. Conveyor 'B' lifts all the goods five hours faster than conveyor 'A' but four hours slower than the conveyor 'C'. The durations of time required to lift all the goods, individually by the conveyors 'A', 'B' and 'C' are
General Mental Ability, Quantitative Aptitude and StatisticsTime, work and measurement
- A17, 12, 8 hrs.
- B15, 10, 6 hrs.
- C16, 11, 7 hrs.
- D14, 9, 5 hrs.
Explanation
Let B alone take x hours; then A takes x+5 and C takes x−4. Since A and B together do the work in the same time as C alone: 1/(x+5) + 1/x = 1/(x−4). Trying x = 10: 1/15 + 1/10 = 5/30 = 1/6 = 1/(10−4). So A = 15 h, B = 10 h, C = 6 h — option (B).