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Question
Divide 184 into two parts such that one-third of one part may exceed one-seventh of another part by 8.
Solution
Let the first part of 184 be x .
Therefore, the other part will be (184 - x) .
According to the question,
\[\frac{1}{3}x - \frac{1}{7}(184 - x) = 8\]
or \[\frac{7x - 552 + 3x}{21} = 8\]
or 10x - 552 = 168 [After cross multiplication]
or 10x = 168 + 552
or \[x = \frac{720}{10} = 72\]
Thus, the parts of 184 are 72 and 112 (184 - 72 = 112) .
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