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. Five friends namely Aman, Bhavya, Chirag, Deepak, and Eshan, went for dinner. Find the total amount paid by Bhavya and Deepak together. Statement I: Amount paid by Aman, Chirag, and Eshan formed a geometric progression in the same order with common ratio 1.25, whereas total amount paid by the same three persons together was Rs. 12,200. Statement II: Total amount paid by Bhavya, Chirag, and Deepak formed an arithmetic progression in the same order with common difference of 500. Statement III: Amount paid by Aman and Bhavya together was Rs. 2,200 more than that paid by Deepak whereas the amount paid by Deepak was Rs. 500 less than that paid by Eshan. Total amount paid by all of them together was Rs. 20,200.

Statement I: Sum of Geometric progression with first term 'a' and common ratio 'r' = [{a X (rⁿ - 1) }/(r - 1) ] {Where 'n' is the number of terms.} So, 12200 = {a X (1.25³ - 1) /(0.25) } Or, 3.8125a = 12200 Or, a = 3200 So, Amount paid by Aman = Rs. 3,200 Amount paid by Chirag = 3200 X 1.25 = Rs. 4,000 And, Amount paid by Eshan = 4000 X 1.25 = Rs. 5,000 But we cannot find the sum of amount paid by Bhavya and Deepak. So, data in statement I alone is not sufficient to answer the question. Statement II: According to statement; Amount paid by Bhavya = Rs. 'Q' Amount paid by Chirag = Rs. (Q + 500) Amount paid by Deepak = Rs. (Q + 1,000) But we cannot find the sum of amount paid by Bhavya and Deepak. So, data in statement II alone is not sufficient to answer the question. Statement III: Let amount paid by Aman, Bhavya, Chirag, Deepak and Eshan be P, Q, R, S and T respectively. According to statement; (P + Q) = S + 2200 .... (I) And, S = T - 500 Or, T = S + 500 .... (II) Also, P + Q + R + S + T = 20,200 Using (I) and (II), we have; S + 2200 + R + S + S + 500 = 20200 Or, 3S + R = 17500 ...... (III) But we cannot find the sum of amount paid by Bhavya and Deepak. So, data in statement III alone is not sufficient to answer the question. On combining statement I and II, we have; Amount paid by Chirag = Rs. 4,000 So, amount paid by Bhavya = 4000 - 500 = Rs. 3,500 Amount paid by Deepak = 4000 + 500 = Rs. 4,500 Required sum = 3500 + 4500 = Rs. 8,000 So, data given in statement I and II together is sufficient to answer the question. On combining statements I and III: 3S + R = 17500 3S = 17500 - 4000 3S = 13,500 S = 4,500 So, T = S + 500 = 5,000 So, amount paid by Bhavya = 20,200 - 3200 - 4000 - 4500 - 5000 = Rs. 3,500 Required sum = 3500 + 4500 = Rs. 8,000 So, data given in statement I and III together is sufficient to answer the question. On combining statement II and III we have; 3S + R = 17500 3S + (S - 500) = 17500 4S - 500 = 17500 4S = 18,000 S = 4,500 So, Q = 4,500 - 1,000 = 3,500 Required sum = 3500 + 4500 = Rs. 8,000 So, data given in statement II and III together is sufficient to answer the question. Therefore, the data given in any of the two statements combined together is sufficient to answer the question.