It takes six days for three women and two men working together to complete a work. Three men would do the same work five days sooner than nine women. How many times does the output of a man exceed that of a woman?

Mini and Vinay are quiz masters preparing for a quiz. In $x \mathrm{minutes}$, Mini makes $y$ questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in $x \mathrm{minutes}$ Mini would make $2y$ questions more than Vinay. How many questions does Mini make in $x \mathrm{minutes}$?

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