Understanding the Problem:
In this problem, we are given a string insulator with a certain voltage distribution. The bottom unit of the insulator is receiving 50% of the total voltage, and the overall string efficiency is given as 40%. We need to determine the number of units in the string insulator.

String Efficiency:
The string efficiency of a string insulator is defined as the ratio of the voltage across the bottom unit to the total voltage across all the units. Mathematically, it can be expressed as:

String Efficiency = (Voltage across Bottom Unit / Total Voltage) * 100

Given that the string efficiency is 40%, we can rewrite the equation as:

40 = (Voltage across Bottom Unit / Total Voltage) * 100

Voltage Distribution:
We are also given that the bottom unit receives 50% of the total voltage. Let's assume the total voltage across all the units is V. Therefore, the voltage across the bottom unit is 0.5V.

We can rewrite the equation for string efficiency using these values:

40 = (0.5V / V) * 100

Simplifying the equation:

40 = 0.5 * 100

40 = 50

Determining the Number of Units:
The equation 40 = 50 is not true, so there is a contradiction in the given information. It is not possible to have a string efficiency of 40% when the bottom unit is receiving 50% of the total voltage. Therefore, there is an error in the problem statement or the given values.

However, if we assume that the bottom unit receives 40% of the total voltage and the string efficiency is 40%, we can solve the problem.

Let's assume the total voltage across all the units is V. Therefore, the voltage across the bottom unit is 0.4V.

We can rewrite the equation for string efficiency using these values:

40 = (0.4V / V) * 100

Simplifying the equation:

40 = 0.4 * 100

40 = 40

Conclusion:
In conclusion, the given information in the problem statement is contradictory. However, if we assume that the bottom unit receives 40% of the total voltage and the string efficiency is 40%, the number of units in the string insulator cannot be determined from the given information.