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 $c$.
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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
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Best Answer

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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