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Rs. 559 is divided into $a, b$ and $c$ in such a way that $2 \times$ part of $a=3 \times$ part of $b=4 \times$ part of $c$, then find the part of $c$.

(a) Rs. 129

(b) Rs. 559

(c) Rs. 42

(d) Rs. 43

Solution :

Let $2 a=3 b=4 c=k$ $\therefore \quad a=\frac{k}{2}, b=\frac{k}{3}$ and $c=\frac{k}{4}$

$\therefore$ The L.C.M. of $2,3,4=12$

$\therefore \quad a=\frac{k}{2} \times 12=6$

$b=\frac{k}{3} \times 12=4$

$c=\frac{k}{4} \times 12=3$

Hence $a: b: c=6: 4: 3$

According to question,

\begin{aligned} & a+b+c=6 x+4 x+3 x=559 \\ \Rightarrow \quad & 13 x=559 \\ \Rightarrow \quad & x=\frac{559}{13}=43 \\ \therefore \text { Part of } c=& 3 x=3 \times 43 \\ =& \text { Rs. } 129 ; \text { Ans. } \end{aligned}

$\quad a+b+c=6 x+4 x+3 x=559$ $\Rightarrow \quad 13 x=559$ $\Rightarrow \quad x=\frac{559}{13}=43$ $\therefore$ Part of $c=3 x=3 \times 43$ $\quad=$ Rs. $129 ;$ Ans. $\therefore \quad$ Correct option is$($ a)

 Trick :The ratios of $a: b: c$$\begin{array}{l}=3 \times 4: 4 \times 2: 2 \times 3 \\=6: 4: 3\end{array}$$$\therefore \quad$The part of$c=\frac{3 \times 559}{6+4+3}\$=Rs. 129: Ans.

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