Direction: In the following question, a questions is followed by information given in three statements. You have to study the question along with the statements and decide, the information given in which of the statements (s) is necessary to answer the question.
In how many days can 16 men and 8 women together complete the piece of work?
I. 8 men complete the piece of work in 10 days.
II. 16 women complete the piece of work in 10 days.
III. 5 women take 32 days to complete the piece of work.
Solution
Correct Answer: Option D
Assume that 1 man can complete the work alone in M days.
∴ In 1 day 1 man can do 1÷M part of the work. [Assuming total work = 1 unit]
⇒In 1 day 16 man can do 16÷M part of the work.
1 woman can complete the work alone in W days.
∴ In 1 day 1 woman can do 1÷W part of the work. [Assuming total work = 1 unit]
⇒In 1 day 8 man can do 8÷W part of the work.
If in K days 16 men and 8 women together can complete the piece of work then, [Assuming total work = 1 unit]
\(K\left( {\frac{{16}}{M} + \frac{8}{W}} \right) = 1\)
From statement 1:
8 men complete the piece of work in 10 days.
\(\Rightarrow \frac{{8 \times 10}}{M} = 1\)
⇒ M = 80 days.
From statement 2:
16 women complete the piece of work in 10 days.
\(\Rightarrow \frac{{16 \times 10}}{W} = 1\)
⇒ W = 160 days.
From statement 3:
5 women complete the piece of work in 32 days.
\(\Rightarrow \frac{{32 \times 5}}{W} = 1\)
⇒ W = 160 days.
From statement 1 & 2 or 1 & 3:
M = 80 days & W = 160 days.
We know that,
\(K\left( {\frac{{16}}{M} + \frac{8}{W}} \right) = 1\)
\(\Rightarrow K\left( {\frac{{16}}{{80}} + \frac{8}{{160}}} \right) = 1\)
⇒ K = 4
∴ In 4 days 16 men and 8 women together complete the piece of work.
∴ Only I and either II or III required to solve the question.
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