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 ratio of the total games win by A and the total games lose by C.

The correct option is 1:1.

Let's break down the information given in the problem step-by-step to find all the necessary values.

Step 1: Information for Person B

Total games won by B = 50.

Step 2: Information for Person A

We are given that the average of the number of games lost by A and games won by B is 105.

Average = (Games lost by A + Games won by B) / 2

105 = (Games lost by A + 50) / 2

Games lost by A + 50 = 210

Games lost by A = 210 - 50 = 160.

We are given that the ratio of total games lost by A to total games won by A is 4 : 3.

Ratio of (Games lost by A) : (Games won by A) = 4 : 3

Since 4 parts correspond to 160 games lost by A:

1 part = 160 / 4 = 40

Games won by A = 3 parts = 3 × 40 = 120.

Step 3: Finding games lost by B

The ratio of games won by A to games lost by B is given as 3 : 2.

Ratio of (Games won by A) : (Games lost by B) = 3 : 2

Since 3 parts correspond to 120 (Games won by A):

1 part = 120 / 3 = 40

Games lost by B = 2 parts = 2 × 40 = 80.

Step 4: Information for Person C

Total games won by C is 20% more than the total games lost by B.

Games won by C = 80 + (20% of 80) = 80 + 16 = 96.

The ratio of total games won to lost by C is given as 4 : 5.

Ratio of (Games won by C) : (Games lost by C) = 4 : 5

Since 4 parts correspond to 96 (Games won by C):

1 part = 96 / 4 = 24

Games lost by C = 5 parts = 5 × 24 = 120.

Step 5: Find the required ratio

We need to find the ratio of the total games won by A to the total games lost by C.

Required Ratio = (Games won by A) : (Games lost by C)

Required Ratio = 120 : 120 = 1 : 1.