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.

Total games lose by B is what percentage of the total games win by A?

The correct answer is 66.67%.

Step-by-step breakdown and calculations:

1. Given Information:

• Total games won by B = 50

2. Calculate the average of games lost by A and games won by B:

The average of games lost by A and games won by B is given as 105.

$\frac{(Games\; lost\; by\; A)\; +\; (Games\; won\; by\; B)}{2}=105$

$(Games\; lost\; by\; A)\; +\; 50=210$

$Games\; lost\; by\; A=210-50=160$

3. Calculate total games won by A:

The ratio of total games lost by A to total games won by A is 4 : 3.

$\frac{\text{Games lost by A}}{\text{Games won by A}}=\frac{4}{3}$

$\frac{160}{\text{Games won by A}}=\frac{4}{3}$

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

4. Calculate total games lost by B:

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

$\frac{\text{Games won by A}}{\text{Games lost by B}}=\frac{3}{2}$

$\frac{120}{\text{Games lost by B}}=\frac{3}{2}$

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

5. Calculate required percentage:

We need to find what percentage of the total games won by A is total games lost by B.

$\text{Percentage}=\left(\frac{\text{Games lost by B}}{\text{Games won by A}}\right)\times 100$

$\text{Percentage}=\left(\frac{80}{120}\right)\times 100=\left(\frac{2}{3}\right)\times 100=66.67\%$