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 and 16 women can do the work together, they can complete the whole work in 53⅓ days. (z+24) girls and 10 men and 14 women together can do the same work in 16 days. If z girls worked together the same work completed in 26 days, then find the value of z.
- A.
55
- B.
80
- C.
95
- D.
100
- E.
75
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
In a work problem, each worker's one-day output (rate) is the total work divided by (number of workers x days they would take alone). If a group finishes a fixed work W, then (sum of all rates) x (days) = W. A key consequence here: when 'p men finish in q days' and 'q women finish in p days' describe the SAME work, one man and one woman turn out to have the identical daily rate.
Application
One man's rate = W / (p x q), since p men working q days give the whole work W. One woman's rate = W / (q x p) for the same reason. These are equal, so a man and a woman each do the same amount of work per day.
Take total work W = p x q units, so each man and each woman does 1 unit per day. The 20 men + 16 women = 36 equal workers finish in 53⅓ = 160/3 days, so W = 36 x 160/3 = 1920 units. Thus p x q = 1920, and the 10 men + 14 women = 24 workers together do 24 units per day.
Let each girl's daily output be g units. The (z + 24) girls together with the 24 men+women finish in 16 days: 16 x [ (z + 24)g + 24 ] = 1920, which gives (z + 24)g = 96.
The z girls alone finish in 26 days: 26 x z x g = 1920, so z x g = 960/13.
Subtract z x g from (z + 24)g: 24g = 96 - 960/13 = 288/13, so g = 12/13 unit/day. Then z = (z x g) / g = (960/13) / (12/13) = 80.
Cross-check
Put z = 80 and g = 12/13 back in: 80 girls in 26 days deliver 26 x 80 x 12/13 = 1920 units, and (80 + 24) girls plus the 24 men+women in 16 days deliver 16 x (104 x 12/13 + 24) = 16 x (96 + 24) = 1920 units. Both equal the total work, confirming z = 80.