Ratios & Proportion
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Q.

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.133

 C.

Rs.144

 D.

Rs.128

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Solution:
Option(C) is correct

8 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, 12 and 6 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, 12 and 6 is 24.

Therefore, the ratio $A:B:C$ is

 \(\dfrac{24}{8}:\dfrac{24}{12}:\dfrac{24}{6}\Rightarrow A:B:C::3:2:4\)

The sum of the total wages

=$3x+2x+4x=432$ 

$9x=432$ or $x=48$.

Hence $A$ gets $3×48$= Rs \(144\)

Edit: For an alternative solution, check comment by Sravan Reddy.


(6) Comment(s)


Anant
 ()

8A=12B => A:B=3:2

12B=6C=> B:C=1:2

so A:B:C=3:2:4

From here you can find the rest of the solution



Disha
 ()

x + y + z = 432 ------ (1)

8x = 12y >> so x = 3y/2

y = 2x/3

8x=6z >>> so x = 3z/4

so , z = 4z/3

Put all value in eq. 1.

x + 2x/3 + 4z/3 = 432

9x= 432*3

x= 144



Vijay
 ()

choice c

8a=12b=6c

and a+b+c = 432

solving for a=144 b= 96 c= 192



Priyanka
 ()

why lcm we should please explain



Sravan Reddy
 ()

8 times A = 12 times B

Suppose A:B is $12:8$ then $8*12x = 12*8x$ =TRUE

Suppose A:B is $8:12$ then $8*8x = 12*12x$ -> Clearly FALSE

Also 8 times A = 12 times B means A is clearly bigger, so $8:12$ can't be the case.

Now, whenever the problem is like this, they should be inverse ratios.

So, Instead of $8:12:6$, it will be $\dfrac{1}{8}:\dfrac{1}{12}:\dfrac{1}{6}$



Bhaumik
 ()

why is it no 8:12:6 ?