A garrison of 300 soldiers had food stock sufficient for 30 days when the rate of consumption is 2.5 kg/day/soldier. After some days of consumption at the rate, 150 soldiers were transferred to another garrison and the rest of food lasted for 30 days for the remaining soldiers. If the rate of consumption is 3 kg/day/soldier, after how many days from the start, were the soldiers transferred?

A garrison of 300 soldiers had food stock sufficient for 30 days when the rate of consumption is 2.5 kg/day/soldier. After some days of consumption at the rate, 150 soldiers were transferred to another garrison and the rest of food lasted for 30 days for the remaining soldiers. If the rate of consumption is 3 kg/day/soldier, after how many days from the start, were the soldiers transferred? Correct Answer 12

Total food = 300 × 30 × 2.5 = 22500 kg

Let the days after which the transfer occurred be ‘x’ days

Food left = 22500 - 300 × 2.5 × x

This is same as food lasted for the rest of garrison

Food left = 150 × 30 × 3 = 13500 kg

22500 - 300 × 2.5 × x = 13500