Question

During a particular stage of the growth of a crop, consumptive use of water is \(2\) to \(8\) mm/day. If the amount of water available in the soil is \(25\%\) of \(80\) mm depth of water. What is the minimum and maximum frequency of irrigation?

• A. \(2.5\) days and \(20\) days
• B. \(2.5\) days and \(10\) days
• C. \(5\) days and \(10\) days
• D. \(5\) days and \(20\) days

Hint:

Use \[ \boxed{ F=\frac{\text{Available Water}}{\text{Consumptive Use}} } \] Higher consumptive use gives smaller irrigation interval.

Answer 1

The Correct Option is B

Concept: The frequency of irrigation is given by \[ \boxed{ F=\frac{\text{Available Soil Moisture}}{\text{Consumptive Use}} } \] where \[ F=\text{Frequency of irrigation (days)}. \]

Step 1: Calculate the available soil moisture. Available water \[ =25\%\times80 =\frac{25}{100}\times80 =20\text{ mm} \]

Step 2: Calculate minimum frequency. Maximum consumptive use \[ =8\text{ mm/day} \] Hence, \[ F_{\min} =\frac{20}{8} =2.5\text{ days} \]

Step 3: Calculate maximum frequency. Minimum consumptive use \[ =2\text{ mm/day} \] Hence, \[ F_{\max} =\frac{20}{2} =10\text{ days} \] Therefore, \[ \boxed{F_{\min}=2.5\text{ days},\qquad F_{\max}=10\text{ days}.} \] Hence, the correct option is \[ \boxed{(B)\;2.5\text{ days and }10\text{ days}.} \]