‘A’, ‘B’, ‘C’, ‘D’ and ‘E’ are five

Solution

For I: Let the present age of ‘A’ = x years Present age of ‘C’ = 2x years Sum of the present ages of ‘B’ and ‘C’ = 36 × 2 = 72 years Present age of ‘B’ = (72 – 2x) years Present age of ‘D’ = [(72 – 2x)/6] × 13 years After eight years, the age of ‘A’ = (x + 8) years After eight years, the age of ‘E’ = [(x + 8)/7] × 13 years Present age of ‘E’ = [(x + 8)/7] × 13 – 8 years Sum of the ages of ‘A’, ‘D’ and ‘E’ = (40 × 5) – 72 = 128 years x + {[(72 – 2x)/6] × 13} + {[(x + 8)/7] × 13} - 8= 128 x + (936 – 26x)/6 + (13x + 104)/7 - 8= 128 42x + 6552 – 182x + 78x + 624 – 336 = 128 × 42 62x = 1464 x = 1464/62 Therefore, I cannot be true. For II: Let the present age of ‘A’ = x years Present age of ‘C’ = 2x years Sum of the present ages of ‘B’ and ‘C’ = 32 × 2 = 64 years Present age of ‘B’ = (64 – 2x) years Present age of ‘D’ = [(64 – 2x)/6] × 13 years After eight years, the age of ‘A’ = (x + 8) years After eight years, the age of ‘E’ = [(x + 8)/7] × 13 years Present age of ‘E’ = [(x + 8)/7] × 13 – 8 years Sum of the ages of ‘A’, ‘D’ and ‘E’ = (36 × 5) – 64 = 116 years x + {[(64 – 2x)/6] × 13} + {[(x + 8)/7] × 13} - 8= 116 x + (832 – 26x)/6 + (13x + 104)/7 - 8= 116 42x + 5824 – 182x + 78x + 624 – 336 = 116 × 42 62x = 1240 x = 20 Present age of ‘E’ = [(x + 8)/7] × 13 – 8 = 44 years Present age of ‘D’ = [(64 – 2x)/6] × 13 = 52 years Difference = 52 – 44 = 8 years Therefore, ‘II’ can be true. For III: Let the present age of ‘A’ = x years Present age of ‘E’ = 2x years Sum of the present ages of ‘B’ and ‘C’ = 20 × 2 = 40 years Present age of ‘A’ = (40 – 2x) years Present age of ‘D’ = [(40 – 2x)/6] × 13 years After eight years, the age of ‘A’ = (x + 8) years After eight years, the age of ‘E’ = [(x + 8)/7] × 13 years Present age of ‘E’ = [(x + 8)/7] × 13 – 8 years Sum of the ages of ‘A’, ‘D’ and ‘E’ = (30 × 5) – 40 = 110 years x + {[(40 – 2x)/6] × 13} + {[(x + 8)/7] × 13} - 8= 110 x + (520 – 26x)/6 + (13x + 104)/7 – 8 = 110 42x + 3640 – 182x + 78x + 624 – 336 = 110 × 42 -62x = 692 x = -692/62 Age cannot be negative. Therefore, III is false.