A work can be completed by 35 workers in 30 days. If 5 workers leave after every 10 days then in how many days will the work be completed?

37.5 days

Formula to be used here,

\( { M}_{1 } \) x \( { D}_{1 } \)  = \( { M}_{2 } \) x \( { D}_{2 } \)

where, M = No. of Men, D = No. of days,

⇒ Total work = 35 x 30 = 1050 units,  

⇒ Starting with 35 men, after every 10 days, 5 men left the work,

⇒ Therefore, (35 x 10) + (30 x 10) + (25 x 10) = 350 + 300 + 250 = 900 units,

⇒ Remaining work = 1050 - 900 = 150 units,

⇒ Time required by 20 men to complete 150 units of work = \(\frac{150}{20}\) = 7.5 days,    ..(\(\frac{Work}{Efficiency}\) = Time)

⇒ Therefore, total time taken by them to complete the work = 30 + 7.5 = 37.5 days.