15 men can complete a work in 280 days. They started the work and after every 10 days, 15 additional men were employed. In how many days the work was completed?

Initial Men = 15. These 15 men can finish the work in 280 days. Total Work = 15 * 280 men-days days = 4200 men- days They work for 10 days. So, work done = 15*10 men-days. Now 15 more men were added, and they worked for 10 days= 30*10 men days Similarly for the next days 15*10+ 30*10+………….+ nth term = 15*280 10(15 + 30 + ..............nth term) = 15*280 So, this makes an AP. Sum= (n/2) *{2a + (n-1)d} Where n is the nth term, a= first element, d is the difference 15* 280= 10[(n/2) *{2*15 +(n-1)15}] 15*28 = (n/2)*(15+ 15n) 30*28 15n+ 15n² n²+n = 56 So, n = 7, -8 (but n cannot be negative) So, n=7 It means 7*10 = 70 days So, work will be done in 70 days.