Read the following data carefully and answer the questions given below. The data shows the three different people (A, B & C) win or lose multiple games.

Total games win by B is 50 and the ratio of game win by A and games lose by B is 3:2 respectively. The ratio of total games loses by A to total games win by A is 4:3. The average of number of games lose by A and win by B is 105. Total games win by C is 20% more than total games loss of B and the ratio of total games win to lose by C is 4 : 5.

Find the sum of total games lose by B and A.

The correct option is 240.

Let us analyze the given information step-by-step to find the required values for each person:

1. Given Data:
- Total games won by B = 50.

2. Information about Person A & Person B:
- The average of the number of games lost by A and won by B is 105.
$\frac{\text{Games lost by A}+\text{Games won by B}}{2}=105$

Substituting the value of games won by B (50):
$\text{Games lost by A}+50=210$
$\text{Games lost by A}=210-50=160$

- The ratio of total games lost by A to total games won by A is 4 : 3.
$\frac{\text{Games lost by A}}{\text{Games won by A}}=\frac{4}{3}$

Using Games lost by A = 160:
$\frac{160}{\text{Games won by A}}=\frac{4}{3}$
$\text{Games won by A}=\frac{160\times 3}{4}=120$

- The ratio of games won by A to games lost by B is 3 : 2.
$\frac{\text{Games won by A}}{\text{Games lost by B}}=\frac{3}{2}$

Using Games won by A = 120:
$\frac{120}{\text{Games lost by B}}=\frac{3}{2}$
$\text{Games lost by B}=\frac{120\times 2}{3}=80$

3. Required Calculation:
We need to find the sum of total games lost by B and A:
$\text{Sum}=\text{Games lost by B}+\text{Games lost by A}$
$\text{Sum}=80+160=240$

Thus, the sum of total games lost by B and A is 240.