A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?
- 5 days
- 10 days
- 15 days
- 20 days
- 25 days
The Usual Method
Total provision is equivalent to 900 x 40 = 36,000 man days
Of this total, 900 x 20 = 18,000 man days worth of provision is already consumed in the first 20 days by the 900 men.
Hence balance provision is equivalent to 36,000 – 18,000 = 18,000 man days.
With 300 more men joining, total number of men in the fort = 900 + 300 = 1200 men.
Let ‘x’ be the number of days for which the provision would last from the day the 300 men joined in.
Hence total number of new man days = = man days.
This should be equivalent to 18,000 man days.
Estimated Time to arrive at the answer = 45 seconds.
Since 20 days worth of provision is already consumed, the balance provision would last for 40 – 20 = 20 more days. Since 300 more men joining there is a % increase.
Hence to keep the total consumption constant, the number of days has to be reduced by 25%. (See concept explained in section of Percentage in Stuff to Remember)
A 25% reduction on the balance 20 days results in 20 – 5 = 15 days.
Estimated Time to arrive at the answer = 15 seconds.