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The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is____________?

Correct answer: B. Rs. 4000

  • A. Rs. 3500
  • B. Rs. 4000
  • C. Rs. 4050
  • D. Rs. 5000Downloading Interactive Party Trivia Games

Explanation

The pair totals are P + Q = 2 x Rs. 5050 = Rs. 10,100, Q + R = Rs. 12,500, and P + R = 2 x Rs. 5200 = Rs. 10,400. Adding the first and third equations and subtracting the second gives 2P = Rs. 10,100 + Rs. 10,400 - Rs. 12,500 = Rs. 8,000, so P earns Rs. 4,000 per month. The likely mistake is choosing Rs. 3,500 by subtracting the averages without first converting them to pair totals.

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An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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