There is a provision of food for 50 days of 500 soldiers in a Fort. How many soldiers should leave after 30 days so that the remaining food may last for another 25 days for the remaining soldiers?
Answers
Answer:
Step-by-step explanation:
There is enough food for 500 soldiers for 30 days. Say that each soldier has one unit of food a day. So there are 500 units for one day and 500 × 30 = 15000 units for the 30 days. So as per the question after 6 days some soldiers left the fort, it means 500 × 6 = 3000 units are consumed by the time some soldiers left. Total unit left = 15000 - 3000 = 12000 units. Now we know that x units are consumed a day, and the food lasted for 32 days more. so the following formula is used to solve this problem.
Number of soldiers left × Days of food will last = Unit of left
x × 32 = 12000
x = 12000 ÷ 32
x = 375
375 soldiers left in the fort.
500 - 375 = 125 soldiers had left the fort.
Answer:
After 15 days, provision lasts for (50 - 15) i.e. 35 days for 1000 soldiers.
Let the food may last for 40 days for
x
soldiers.
No. of days the No. of soldiers
food last
35 1000
40
x
Here, the number of days is inversely related to the number of soldiers. So as the days increases, the number of soldiers will decrease.
∴
40
:
35
::
1000
:
x
⇒
40
35
=
1000
x
Cross-multiplying, we get
⇒
40
×
x
=
1000
×
35
⇒
x
=
1000
×
35
40
=
875
Hence, the number of soldiers left = 1000 - 875 = 125