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      Question

      The question consists of three statements numbered

      “I, II and III” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. There are 4 persons i.e. ‘P’, ‘Q’, ‘R’ and ‘S’. Find the income of ‘R’. Statement I: The average of incomes of ‘P’, ‘Q’ and ‘R’ is Rs. 16000, while income of ‘S’ is Rs. 18000 more than that of ‘P’. Statement II: The ratio of incomes of ‘P’ and ‘S’ is 2:5, respectively, and sum of incomes of ‘P’ and ‘Q’ is Rs. 36000. Statement III: Q’s income is twice that of R’s and Rs. 6000 less than that of S’s.
      A The data in statement I and statement II together is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      B The data in statement II and statement III together is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C The data in statement I and statement III together is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      D The data in all statements I, II and III together is necessary to answer the question. Correct Answer Incorrect Answer
      E The data in any of the two statements together is sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      Let, income of ‘P’ = Rs. p Income of ‘Q’ = Rs. q Income of ‘R’ = Rs. r Income of ‘S’ = Rs. s Statement I: (p + q + r) = 16000 × 3 = Rs. 48000 s = (p + 18000) Therefore, statement I alone is not sufficient to answer the question. Statement II: (p/s) = 2/5 And, p + q = 36000 Therefore, statement II alone is not sufficient to answer the question. Statement III: Q’s income is twice that of ‘R’ and Rs. 6000 less than that of ‘S’. Therefore, statement III alone is not sufficient to answer the question. Combining statement I and II: So, p + q + r = 48000 s = p + 18000 p/s = 2/5 p = 2s/5 s - 2s/5 = 18000 3s/5 = 18000 s = 30000 p = 2 × 30000/5 = 12000 Also, p + q = 36000 q = 36000 - 12000 = 24000 12000 + 24000 + r = 48000 r = 12000 So, statement I and II together is sufficient to answer the question. Combining Statement II and III: p/s = 2/5 p = 2s/5 p + q = 36000 Or, q = s - 6000 And, q = 2r Therefore, (2s/5) + s - 6000 = 36000 Or, 7s/5 = 42000 Or, 7s = 210000 Or, s = 30000 So, q = s - 6000 = 24000 Or, r = q/2 = 12000 So, statement II and III together is sufficient to answer the question. Combining Statement I and III: So, p + q + r = 48000 s = p + 18000 And, q = 2r Also, q = s - 6000 So, p = s - 18000 q = s - 6000 r = (s - 6000)/2 Therefore, s - 18000 + s - 6000 + (s - 6000)/2 = 48000 2s - 24000 + (s - 6000)/2 = 48000 4s - 48000 + s - 6000 = 96000 5s - 54000 = 96000 5s = 150000 Or, s = 30000 Or, q = s - 6000 = 24000 So, r = q/2 = 12000 So, statement I and III together is sufficient to answer the question. Therefore, data in any of the two statements together is sufficient to answer the question.

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