AFCAT Model Paper 5

Given: Number of days for which food provided = 30 days Number of people who left $= \frac{1}{5}$ Calculation: Let the food consumed by 1 man in 1 day be x and total men be y Let the time after which people left be z days Then the total quantity of food = 30xy Food consumed by y men in z days = xyz Remaining food = 30xy - xyz = xy(30 - z) After z days, total men $= \frac{4y}{5}$ Food consumed by $\frac{4y}{5}$ men in 1 day $= \frac{4xy}{5}$ Time taken for 4y/5 men to consume remaining food $= \frac{xy(30 - z)}{\frac{4xy}{5}} = \frac{5(30 - z)}{4}$ $\Rightarrow \frac{5(30 - z)}{4} = 30$ ⇒ z = 6 days