The one-day work of 2 men is equal to the one-day work of 4 women or the one-day work of 8 qualified workers. 10 qualified workers can finish a work in 8 days. If a man, a woman and a qualified worker work in the same order on three different days, the work is finished in ________ days.
- A5
166
- B6
203
- C4
131
- D4
135
Solution & Step-by-step Explanation
From efficiency relations:
2M=4W=8Q⟹1M=2W=4Q
Let the efficiency of a qualified worker (Q) = 1 unit/day.
Then efficiency of a woman (W) = 2 units/day.
Efficiency of a man (M) = 4 units/day.
Total work = Efficiency of 10Q×8 days=(10×1)×8=80 units.
They work alternately:
Day 1: Man (M) works = 4 units
Day 2: Woman (W) works = 2 units
Day 3: Qualified worker (Q) works = 1 unit
Total work done in 1 cycle of 3 days = 4+2+1=7 units.
Number of full cycles = ⌊
7
80
⌋=11 cycles.
Work done in 11 cycles = 11×7=77 units.
Days elapsed so far = 11×3=33 days.
Remaining work = 80−77=3 units.
On Day 34 (next cycle starting with Man), the man can do 4 units per day.
Time taken by man to finish the remaining 3 units =
4
3
day.
Total time = 33+
4
3
=
4
135
days.
2M=4W=8Q⟹1M=2W=4Q
Let the efficiency of a qualified worker (Q) = 1 unit/day.
Then efficiency of a woman (W) = 2 units/day.
Efficiency of a man (M) = 4 units/day.
Total work = Efficiency of 10Q×8 days=(10×1)×8=80 units.
They work alternately:
Day 1: Man (M) works = 4 units
Day 2: Woman (W) works = 2 units
Day 3: Qualified worker (Q) works = 1 unit
Total work done in 1 cycle of 3 days = 4+2+1=7 units.
Number of full cycles = ⌊
7
80
⌋=11 cycles.
Work done in 11 cycles = 11×7=77 units.
Days elapsed so far = 11×3=33 days.
Remaining work = 80−77=3 units.
On Day 34 (next cycle starting with Man), the man can do 4 units per day.
Time taken by man to finish the remaining 3 units =
4
3
day.
Total time = 33+
4
3
=
4
135
days.