Read the following data carefully and answer the questions given below. The…
2024
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 average of total games win by A & B and total games lose by C.
- A.
98.25
- B.
91.67
- C.
83.33
- D.
96.67
- E.
129
Show answer & explanation
Correct answer: D
Concept
In data-interpretation chain problems, every unknown is pinned by working the given ratios and averages in the right order. Two identities drive this set: an average of two quantities equals their sum divided by 2, and a ratio a:b lets you scale one quantity from the other. Start from the one fully-known value and propagate.
Application
Games won by B is given as 50.
The average of (games lost by A) and (games won by B) is 105, so their sum is 210; subtracting B's 50 wins gives games lost by A = 160.
Games lost by A : games won by A = 4 : 3, so games won by A = 160 × 3/4 = 120.
Games won by A : games lost by B = 3 : 2, so games lost by B = 120 × 2/3 = 80.
Games won by C is 20% more than games lost by B = 80 × 1.2 = 96.
Games won by C : games lost by C = 4 : 5, so games lost by C = 96 × 5/4 = 120.
Required average = (games won by A + games won by B + games lost by C) / 3 = (120 + 50 + 120) / 3 = 290 / 3 = 96.67.
Cross-check
Re-trace the dependency: 160 lost by A scaled by 3/4 gives 120 won by A; 120 scaled by 2/3 gives 80 lost by B; 80 grown by 20% gives 96 won by C; 96 scaled by 5/4 gives 120 lost by C. The three target quantities 120, 50 and 120 sum to 290, and 290 ÷ 3 = 96.67, confirming the result.