Question

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the
other part by 8.
Hint. Let the two parts be x and (184 - x). Then,
--*--184-) = 8.​

Answer 1

Let one part be x

other part = (184-x)

1/3rd of one part exceeds 1/7th of the other by 8. Thus

(1/3 × x) - [1/7 × (184-x)] = 8

⇒ x/3 - (184/7 - x/7) = 8

⇒ x/3 - 184/7 + x/7 = 8

⇒ x/3 + x/7 - 184/7 = 8

⇒ x/3 + x/7 = 8 + 184/7

⇒ (7x+3x)/21 = (56+184)/7

⇒ 10x/21 = 240/7

⇒ x = 240/7 × 21/10

⇒ x = 72

So one part = 72

other part = 184 - 72 = 112

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