Answer the following question based on the information provided.

Two automated assembly units, Unit A and Unit B, working together can complete a manufacturing order in ‘T’ hours. The production efficiencies of Unit A and Unit B are in the ratio of 5 : 6, respectively. If Unit A starts the operation alone and runs for 11 hours before Unit B joins to help, they together complete the remaining manufacturing work in 31 hours. What is the value of ‘T’?

The correct option is 36.

Step-by-step Explanation:

1. Understand the Efficiency Ratio:

The production efficiencies of Unit A and Unit B are given in the ratio 5 : 6.

Let the work done by Unit A in 1 hour be 5 units.

Let the work done by Unit B in 1 hour be 6 units.

2. Calculate the Total Work Required:

Unit A works alone for 11 hours.

Work done by Unit A in 11 hours:

$\text{Work done by A}=11\×5=55\text{units}$

After 11 hours, Unit B joins Unit A, and together they work for 31 hours to complete the remaining work.

Combined efficiency of Unit A and Unit B per hour:

$\text{Combined efficiency}=5+6=11\text{units/hour}$

Work done by Unit A and Unit B together in 31 hours:

$\text{Remaining work}=31\×11=341\text{units}$

Total work of the manufacturing order:

$\text{Total Work}=55+341=396\text{units}$

3. Calculate the value of 'T':

'T' is the time in hours taken by Unit A and Unit B working together to complete the total manufacturing order from scratch.

Time 'T' is given by:

$T=\frac{\text{Total Work}}{\text{Combined Efficiency}}$

$T=\frac{396}{11}=36\text{hours}$

Therefore, the value of ‘T’ is 36.