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.

**Question:** Find the average of total games won by A and B and total games lost by C.

Question

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.

**Question:** Find the average of total games won by A and B and total games lost by C.

Accepted Answer

**Solution:**

1. Let the games won by A = 3x and games lost by B = 2x (from the ratio 3:2).

2. Given games won by B = 50.

3. Average of games lost by A and games won by B is 105:
   $$\frac{	ext{Lost by A} + 50}{2} = 105 \implies 	ext{Lost by A} = 210 - 50 = 160$$

4. Ratio of lost to won games by A is 4:3:
   $$\frac{	ext{Lost by A}}{	ext{Won by A}} = \frac{4}{3} \implies \frac{160}{3x} = \frac{4}{3}$$
   Solving for x:
   $$160 	imes 3 = 4 	imes 3x \implies 480 = 12x \implies x = 40$$

5. Therefore, games won by A = 3x = 3 	imes 40 = 120.

6. Games lost by B = 2x = 2 	imes 40 = 80.

7. Total games won by C are 20% more than games lost by B:
   $$	ext{Won by C} = 80 + 0.2 	imes 80 = 80 + 16 = 96$$

8. Ratio of games won to lost by C is 4:5:
   $$\frac{96}{	ext{Lost by C}} = \frac{4}{5} \implies 	ext{Lost by C} = \frac{96 	imes 5}{4} = 120$$

9. Required average =
   $$\frac{	ext{Won by A} + 	ext{Won by B} + 	ext{Lost by C}}{3} = \frac{120 + 50 + 120}{3} = \frac{290}{3} = 96.67$$

**Answer:** 96.67

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