Question : Rs. 864 is divided among A, B, and C such that 8 times A's share is equal to 12 times B's share and also equal to 6 times C's share. How much did B get?
Option 1: Rs. 399
Option 2: Rs. 192
Option 3: Rs. 288
Option 4: Rs. 72
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Correct Answer: Rs. 192
Solution :
Let A's share as a, B's share as b, and C's share as c.
Given that 8 times A's share is equal to 12 times B's share and also equal to 6 times C's share,
$8a = 12b = 6c$
$ \frac{1}{3}a = \frac{1}{2}b = \frac{1}{4}c$ ____(i)
Also, we know that the total amount of Rs. 864 is divided among A, B, and C.
$a + b + c = 864$ ____(ii)
Substituting a and c from the equation (i) in (ii),
$\frac{3}{2}b + b + 2b = 864$
⇒ $\frac{3}{2}b + 3b = 864$
⇒ $3b+6b=1728$
⇒ $9b=1728$
⇒ $b=192$
Hence, the correct answer is Rs. 192
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