Question

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

Answer 1

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,

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

$a+b+c=6 x+4 x+3 x=559$ $\Rightarrow \quad 13 x=559$ $\Rightarrow \quad x=\frac{559}{13}=43$

$\therefore$ Part of $c=3 x=3 \times 43$ $\quad=$ Rs. $129 ;$

$\therefore$ Correct option will be (A).