Discussion
Number 198 is divided into three parts such that \(\frac{1}{2}\) of the first part, \(\frac{1}{3}\)rd of the second part and \(\frac{1}{4}\)th of the third part shall all be equal. Then the value of the largest part will be :
Answer: C
The largest part is 88.
Let the common value be k. Then half the first part is k, a third of the second is k and a quarter of the third is k, so the parts are 2k, 3k and 4k:
\[ \begin{aligned} 2k + 3k + 4k &= 198 \\ 9k &= 198 \Rightarrow k = 22 \end{aligned} \]
The parts are 44, 66 and 88, and the largest is 88. Check: 44/2 = 66/3 = 88/4 = 22. 68, 78 and 98 do not give equal fractions.
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