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a, b, c are three natural numbers such that a x b x c = 27846. If a/6 = b + 4 = c - 4, find a + b + c. |
Answer» a ×b × c = 27846 ...... (1) a/b = b + 4 = c - 4 a = 6b + 24 b = b c = b + 8 Put value of a, b, c in (1) (6b + 24) (b) (b + 8) = 27846 6(b + 4) (b) (b + 8) = 27846 (b + 4) (b) (b + 8) = 4641 = 13 × 17 × 3 × 7 = 13 × 17 × 21 ∴ b = 13 a = 6 × 13 + 24 = 78 + 24 = 102 c = b + 8 = 13 + 8 = 21 ∴ a + b + c = 102 + 13 + 21 = 136 |
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