The average price of two items, 'A' and 'B,' is Rs. 960, while the mean price of items 'B' and 'C' is Rs. 1,020. Additionally, the average price of items 'A' and 'C' is Rs. 975. Determine the price of item 'C'.

ATQ,

Let the price of items ‘A’, ‘B’ and ‘C’ be Rs. ‘p’, Rs. ‘q’ and Rs. ‘r’, respectively. Total price of items ‘A’ and ‘B’ = 960 × 2 = Rs. 1,920 Or, (p + q) = 1920 So, q = 1920 – p -------- (I) Total price of items ‘B’ and ‘C’ = 1020 × 2 = Rs. 2,040 Or, (q + r) = 2040 -------- (II) On putting value of ‘q’ from equation (I) in equation (II), we have; 1920 – p + r = 2040 Or, r – p = 120 So, p = r – 120 -------- (III) Total price of ‘C’ and ‘A’ = 975 × 2 = Rs. 1,950 Or, r + p = 1950 On putting value of ‘p’ from equation (III), we have; r + r – 120 = 1950 Or, 2r = 2070 So, r = 1035 Therefore, price of items ‘r’ = Rs. 1,035 Alternate solution Let the price of article ‘A’, ‘B’ and ‘C’ be Rs. ‘p’, Rs. ‘q’ and Rs. ‘r’, respectively. p + q = 1920 q + r = 2040 r + p = 1950 So, 2(p + q + r) = 5910 Or, p + q + r = 2955 So, price of article ‘r’ = 2955 – 1920 = Rs. 1,035