There are 300 men in a group. They have food for 30 days. After 10 days, 100  more men join the group. Remaining food will last for how many days?

15 days

Initially, men = 300, days = 30 days,

After 10 days,

100 more men are added, 

remaining number of days = 30 - 10 = 20 days 

300 men had provisions for 20 days,

1 man had provisions for (300 x 20) days    {less men, more days}

400 men had provisions for $\frac{300 \times 20}{400}$ days = 15 days 

Hence, the remaining food will last for 15 days.