1.

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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