Correct Answer - Option 3 : C

**Given:**

The total number of persons is 50.

The number of persons goes to work by train is 18.

The number of persons goes to work by bus is 26.

The number of persons goes to work neither by train nor by bus is 8.

**Formulas:**

For two sets A and B,

n(A ᴜ B) = n(A) + n(B) – n(A ∩ B)

where n(A) = number of elements in set A.

n(B) = number of elements in set B.

n(A ∩ B) = number of elements present in both sets A and B.

n(A ᴜ B) = the number of elements present in either of the sets A or B.

**Calculation:**

According to the question,

The total number of persons is 50.

The number of persons goes to work neither by train nor by bus is 8.

The total number of persons who go to work either by train or by bus

⇒ 50 – 8 = 42.

Let n(A) be the number of persons who go to work by train,

n(B) be the number of persons who go to work by bus,

n(A ∩ B) be the number of persons who go to work by train as well as by bus.

n(A ᴜ B) be the number of persons go to work either by train or by bus.

According to the formula,

n(A ᴜ B) = n(A) + n(B) – n(A ∩ B)

42 = 18 + 26 - n(A ∩ B)

⇒ 42 = 44 - n(A ∩ B)

⇒ n(A ∩ B) = 44 – 42 = 2.

The total number of persons go to work by train as well as by bus is 2.

The total number of persons who go to work by train only = 18 – 2 = 16.

The percentage of the total number of people going by train only to the total number of persons:

⇒ (16/50) × 100

⇒ 32%

**∴**** The percentage of the total number of people going by train only to the total number of persons is 32.**