Directions: Read the following passage carefully and answer the questions…
2022
Directions: Read the following passage carefully and answer the questions given below.
p men can do a work in q days and q women can do the same work in p days. If 20 men & 16 women can do the work together, they can complete the whole work in 53⅓ days.
Find the number of days taken by 15 men & 12 women together to complete the work.
- A.
711/9 days
- B.
671/9 days
- C.
791/9 days
- D.
621/9 days
- E.
None of these
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
In time-and-work problems, total work is constant and equals (number of workers) × (one worker's rate) × (time). To compare two crews, first express every worker in a single common unit of work-rate, then use Total work = Effective workers × Days, so the number of days is inversely proportional to the number of effective workers.
Setting up the rates
Let total work be W. From the data:
p men finish in q days, so one man's rate = W/(p×q).
q women finish in p days, so one woman's rate = W/(q×p).
Both equal W/(pq), so one man and one woman work at exactly the same rate — a man and a woman are interchangeable here.
Application
Because men and women are equally efficient, count each person as 1 unit of work-rate.
First crew: 20 men + 16 women = 36 equal units, finishing in 53⅓ = 160/3 days.
Total work W = 36 × 160/3 = 1920 unit-days.
Target crew: 15 men + 12 women = 27 equal units.
Days = W ÷ 27 = 1920 ÷ 27 = 640/9, i.e. 711/9 days.
Cross-check
Inverse-proportion check: keeping the work fixed, days scale as 36/27 = 4/3. So (160/3) × (4/3) = 640/9 = 711/9 days — the same result, confirming the division 1920 ÷ 27 is correct.