A man is twice as fast as a woman and a woman is twice as fast as a bo

1.	A man is twice as fast as a woman and a woman is twice as fast as a boy. If all of them i.e. a man, a woman and a boy can finish a work together in 4 days, in how many days a boy shall do it alone?1). 28 days2). 21 days3). 14 days4). 7 days
Answer» ASSUME the efficiency of a boy = B units/day As a woman is TWICE as fast as a boy so the efficiency of a woman = 2B units/day As a man is twice as fast as a woman so the efficiency of a man = 4B units/day According to the question, all of them i.e. a man, a woman and a boy can finish a work together in 4 days. In 4 days total work done by a man, a woman and a boy = 4 × (B + 2B + 4B) = 28B units. ∴ Total work = 28B units. Time required for a boy to do the whole work alone = $(\FRAC{{Total\;work\;}}{{efficiency\;of\;a\;boy}}\; = \frac{{28B}}{B} = 28\;days)$ Time required for a boy to do the whole work alone = 28 days.

A man is twice as fast as a woman and a woman is twice as fast as a boy. If all of them i.e. a man, a woman and a boy can finish a work together in 4 days, in how many days a boy shall do it alone?1). 28 days2). 21 days3). 14 days4). 7 days

Answer»

ASSUME the efficiency of a boy = B units/day

As a woman is TWICE as fast as a boy so the efficiency of a woman = 2B units/day

As a man is twice as fast as a woman so the efficiency of a man = 4B units/day

According to the question, all of them i.e. a man, a woman and a boy can finish a work together in 4 days.

In 4 days total work done by a man, a woman and a boy = 4 × (B + 2B + 4B) = 28B units.

∴ Total work = 28B units.

Time required for a boy to do the whole work alone = $(\FRAC{{Total\;work\;}}{{efficiency\;of\;a\;boy}}\; = \frac{{28B}}{B} = 28\;days)$

Time required for a boy to do the whole work alone = 28 days.

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