Question

$Rs.432$ is divided amongst three workers A, B and C such that $8$ times A"s share is equal to $12$ times B"s share which is equal to $6$ times C"s share. How much did A get?

• A. Rs. $192$
• B. Rs. $138$
• C. Rs. $144$
• D. Rs. $196$

Answer 1

Answer: (C)

Rs. $144$

Times A"s share $=12$ times B"s share $=6$ times C"s share.
Note that this is not the same as the ratio of their wages being $8:12:6$
In this case, find out the L.C.M of $8,12and6$ and divide the L.C.M by each of the above numbers to get the ratio of their respective shares.
The L.C.M of $8,12and6$ and $6$ is $24$.
Therefore, the ratio $A:B:C::\frac{24}{8}:\frac{24}{12}:\frac{24}{6}$
$\Rightarrow A:B:C::3:2:4$
The sum of the total wages $=3x+2x+4x=432$

$⟹9x=432$

or $⟹x=48$.
Hence, A who gets $3x$ will get $3\times 48=Rs.144$