A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are there in the fort?

• 
  Let there be 'x' men in the beginning so that after 15 days the food for them is left for 45 days.
  
  After adding 500 men the food lasts for only 40 days.
  
  Now (x+500) men can have the same food for 40 days.
  
  Therefore by equating the amount of food we get,
  
  45 * x = (x + 500) * 40
  
  45x = (x+500) * 40
  
  5x = 20,000
  
  x = 4,000
  
  Therefore there are 4,000 men in the fort.
  
• 12 years agoHelpfull: Yes(17) No(5)
• 
  Let the number of Men initially in the fort be: M
  
  Amount of provisions initially be: P
  
  After 15 days, (15/60)*100 % of the provisions is gone : 25% is gone
  
  This leaves 75% of the provisions
  
  
  
  M men consume 75% of P in (60-15) days = 45 days ...(i)
  
  (M+500) men consume 75% of P in 40 days...(ii)
  
  Therefore;
  
  from (i), 1 man will consume 75% of P in 45M days. while
  
  from (ii), 1 man will consume 75% of P in 40(M + 500)days
  
  :. 45M = 40(M + 500)
  Solve for M
  
  45M = 40M + 20000
  
  45M - 40M = 20000
  
  5M = 20000
  
  M = 4000 ans
  
  
• 12 years agoHelpfull: Yes(6) No(1)