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.
20 men & 24 women started working together and they did work for 0.6x days and y number of boys did the remaining work in 0.45x days. If the whole work is completed in x days by y number of boys, then find the value of x.
- A.
28
- B.
50
- C.
45
- D.
25
- E.
40
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
In work problems, the work done by a group equals (number of workers) × (rate per worker) × (number of days). When two groups take the same total man-days to finish a job, one member of either group has the same daily rate. If a body of workers can finish the whole job alone in a known time, their combined daily output equals (total work) ÷ (that time), and any portion of the job they do over a sub-interval is that output multiplied by the sub-interval.
Application
Equal rates: p men finish in q days and q women finish in p days, so each job needs the same man-days as woman-days. Hence one man and one woman do equal work per day; take that common rate as 1 unit/day.
Find the total work: 20 men + 16 women = 36 workers, each 1 unit/day, so 36 units/day. They finish in 53⅓ = 160/3 days, so total work = 36 × 160/3 = 1920 units.
First phase: 20 men + 24 women = 44 workers = 44 units/day, working for 0.6x days, do 44 × 0.6x = 26.4x units.
Boys' rate: the boys can finish the whole 1920 units alone in x days, so together they do 1920/x units/day.
Boys' phase: in 0.45x days the boys do (1920/x) × 0.45x = 864 units, and this equals the remaining work 1920 − 26.4x.
Solve: 864 = 1920 − 26.4x ⇒ 26.4x = 1056 ⇒ x = 40.
Cross-check
With x = 40: first phase 26.4 × 40 = 1056 units; boys do 864 units; 1056 + 864 = 1920 units = the full job. The boys' alone-rate is 1920/40 = 48 units/day, and 48 × (0.45 × 40) = 48 × 18 = 864 units, confirming the split.