50 men can construct a road in 60 days. They started the work together

1.	50 men can construct a road in 60 days. They started the work together. But at the end of every 15th day, 10 men left the work. What part of work was left incomplete at the end of allotted time?1). 1/42). 3/103). 7/104). 17/20
Answer» ? 50 MEN can construct the road in60 days ∴ Part of road constructed by 1 man in 1 DAY $(= \frac{1}{{50 \times 60}} = \frac{1}{{3000}})$ Now, for the first 15 days, all 50 men worked. part of work done in first 15 days $(= 15 \times 50 \times \frac{1}{{3000}} = \frac{1}{4})$ After 15 days, 10 men left the work. ∴For next 15 days 40 men worked, part of work done in next 15 days $(= 15 \times 40 \times \frac{1}{{3000}} = \frac{1}{5})$ Again, 10 men left the work after these 15 days, (i.e. after 30 days in total). ∴ For next 15 days 30 men worked, part of work done in next 15 days $(= 15 \times 30 \times \frac{1}{{3000}} = \frac{3}{{20}})$ Now, after 45 days, 10 more men left the work. ∴ For the LAST 15 days, 20 men worked. part of work done in last 15 days $(= 15 \times 20 \times \frac{1}{{3000}} = \frac{1}{{10}})$ ∴ Part of work finished in all 60 days $(= \frac{1}{4} + \frac{1}{5} + \frac{3}{{20}} + \frac{1}{{10}} = \frac{{14}}{{20}} = \frac{7}{{10}})$ ⇒ Part of work left = 1 – (7/10) = 3/10 Hence 3/10^thpart of work REMAINED incomplete.

50 men can construct a road in 60 days. They started the work together. But at the end of every 15th day, 10 men left the work. What part of work was left incomplete at the end of allotted time?1). 1/42). 3/103). 7/104). 17/20

Answer»

? 50 MEN can construct the road in60 days

∴ Part of road constructed by 1 man in 1 DAY $(= \frac{1}{{50 \times 60}} = \frac{1}{{3000}})$

Now, for the first 15 days, all 50 men worked.

part of work done in first 15 days $(= 15 \times 50 \times \frac{1}{{3000}} = \frac{1}{4})$

After 15 days, 10 men left the work.

∴For next 15 days 40 men worked,

part of work done in next 15 days $(= 15 \times 40 \times \frac{1}{{3000}} = \frac{1}{5})$

Again, 10 men left the work after these 15 days, (i.e. after 30 days in total).

∴ For next 15 days 30 men worked,

part of work done in next 15 days $(= 15 \times 30 \times \frac{1}{{3000}} = \frac{3}{{20}})$

Now, after 45 days, 10 more men left the work.

∴ For the LAST 15 days, 20 men worked.

part of work done in last 15 days $(= 15 \times 20 \times \frac{1}{{3000}} = \frac{1}{{10}})$

∴ Part of work finished in all 60 days $(= \frac{1}{4} + \frac{1}{5} + \frac{3}{{20}} + \frac{1}{{10}} = \frac{{14}}{{20}} = \frac{7}{{10}})$