Two men and a woman are entrusted with a task. The second man needs three hours more to cope with the job than the first man and the woman would need working together. The first man, working alone, would need as much time as the second man and the woman working together. The first man, work- ing alone, would spend eight hours less than the double period of time the second man would spend working alone. How much time would the two men and the woman need to complete the task if they all worked together?

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)

If the king makes a decision error, the maximum reduction in the time of resistance could be

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)

A fort contains a granary, that has $1000$ tons of grains. The fort is under the siege from an enemy army that has blocked off all the supply routes.

The army in the fort has three kinds of soldiers:

Sepoys$\to 2,00,000$

Mantris$\to 1,00,000$

Footies$\to 1,00,000$

$100$ sepoys can hold $5\%$ of the enemies for one month.

$100$ mantris can hold $10\%$ of the enemy for $15$ days.

$50$ footies can hold $5\%$ of the enemy for one month

A sepoy eats $1 kg$ of food per month, a mantri eats $0.5 kg$ of food per month and a footie eats $3 kg$ of food. (Assume $1 ton=1000 kg$)

The king has to make some decisions based on the longest possible resistance that can be offered to the enemy.

If a king select a soldier, he will have to feed him for the entire period of the resistance. The king is not obliged to feed a soldier not selected for the resistance.

(Assume that the entire food allocated to a particular soldier for the estimated length of resistance is redistributed into the king's palace in case a soldier dies and available for other soldiers.)