Read the following data carefully and answer the question given below. Three…
2024
Read the following data carefully and answer the question given below.
Three people (A, B and C) each win or lose multiple games. Total games won by B is 50, and the ratio of games won by A to games lost by B is 3 : 2. The ratio of total games lost by A to total games won by A is 4 : 3. The average of the number of games lost by A and games won by B is 105. Total games won by C is 20% more than total games lost by B, and the ratio of total games won to lost by C is 4 : 5.
Find the sum of total games lost by B and A.
- A.
210
- B.
220
- C.
250
- D.
320
- E.
240
Show answer & explanation
Correct answer: E
Concept
In a chained ratio / averages problem, anchor on the one quantity that is fully fixed by an absolute condition (here an average that involves a known value), then propagate that value through each given ratio in turn. A ratio x : y between two quantities means each is a fixed multiple of a common unit, so once one term is numeric the other follows by simple proportion.
Application
Anchor with the average. The average of (games lost by A) and (games won by B) is 105, and games won by B = 50. So games lost by A = 2 × 105 − 50 = 210 − 50 = 160.
Use lost A : won A = 4 : 3. Lost by A = 160 corresponds to 4 parts, so 1 part = 40 and games won by A = 3 × 40 = 120.
Use won A : lost B = 3 : 2. Won by A = 120 corresponds to 3 parts, so 1 part = 40 and games lost by B = 2 × 40 = 80.
Required sum = (games lost by B) + (games lost by A) = 80 + 160 = 240.
Cross-check
Back-substitute the unit value 40: lost A = 4×40 = 160 and won A = 3×40 = 120 keep the 4 : 3 ratio; won A = 120 and lost B = 80 keep the 3 : 2 ratio; and (160 + 50)/2 = 105 reproduces the given average. The C data (won C = 1.2 × 80 = 96, lost C = 96 × 5/4 = 120) is consistent but not needed for this sum, confirming 240.