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.

If the total games lose by D are 25% more than that of A and the total games win by D are five more than half of the total games win by C, then find the difference between the total games lose and total games win by D.

The correct option is 147.

Let us analyze the given information step-by-step to calculate the total number of games won and lost by each person (A, B, C, and D).

Step 1: Calculate games won and lost by A and B

We are given:

• Total games won by B = 50

• The average of the number of games lost by A and won by B is 105.

Therefore, we can set up the equation for the average:

$\frac{\text{Games lost by A}+\text{Games won by B}}{2}=105$

$\text{Games lost by A}+50=210$

$\text{Games lost by A}=210-50=160$

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

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

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

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

We are also given that the ratio of games won by A to games lost by B is 3 : 2.

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

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

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

Step 2: Calculate games won by C

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

$\text{Games won by C}=80+(20\%\text{of}80)$

$\text{Games won by C}=80+16=96$

Step 3: Calculate games won and lost by D

We are given:

• Total games lost by D are 25% more than that of A.

$\text{Games lost by D}=160+(25\%\text{of}160)$

$\text{Games lost by D}=160+40=200$

• Total games won by D are five more than half of the total games won by C.

$\text{Games won by D}=\frac{96}{2}+5$

$\text{Games won by D}=48+5=53$

Step 4: Find the difference between total games lost and total games won by D

$\text{Difference}=\text{Games lost by D}-\text{Games won by D}$

$\text{Difference}=200-53=147$

Thus, the difference between the total games lost and total games won by D is 147.