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By mistake, instead of dividing Rs 117 among three persons $P$, $Q$ and $R$ in the ratio $\left(\dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{4}\right)$, it was divided in the ratio $2:3:4$. Who gains the most and how much?


$P$, Rs 28


$Q$, Rs 35


$R$, Rs 25


$R$, Rs 27

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Option(A) is correct

 Ratio \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}\)  is equivalent to $6:4:3$

So, in case of correct distribution, $P$ would have got,

$=117 \times \dfrac{6}{6+4+3}$

$=\text{Rs. } 54$

$Q$ would have got,

$=117 \times \dfrac{4}{6+4+3}$

$=\text{Rs. } 36$

and $R$ would have got,

$=117 \times \dfrac{3}{6+4+3}$

$=\text{Rs. } 27$

But actually the money was divided in the ratio $2:3:4$ and shares of $P$, $Q$ and $R$ in this case would be,

For $P$,

$=117 \times \dfrac{2}{2+3+4}$

$=\text{Rs. } 26$

For $Q$,

$=117 \times \dfrac{3}{2+3+4}$

$=\text{Rs. } 39$,

and for $R$,

$=117 \times \dfrac{4}{2+3+4}$

$=\text{Rs. } 52$

Thus $P$ gains,

$=54-26 = 28$,

$Q$ gains,

$=36-39 = -3$ (loss)

and $R$ gains,

$=27-52 = -25$ (loss)

Thus, $P$ gains the most $\text{Rs. 28}$

Hence, option (A) is correct choice.

Edit: After pointing out by Dinesh in the comments, a typo has been corrected and initial money amount has been changed to Rs. 117 instead of Rs. 177.

Edit 2: Correct answer choice has been changed to option (A) from option (C), after it has been pointed out by Charlie.

(9) Comment(s)


Obviously the answer is C. Charlie please read the question properly. Do not mislead others.

Deepak P S

The answer should be option (C)

The money P.Q and R should have got is 54, 36, 27 respectively and what they actually got is 26, 39 and 52 respectively. so, R got 25 more than what he should have got.

Karan Sharma

the answer should be (c)..

here,what they actually received is

P-26,Q-39,R-52..But they were suppose to get,

P-54,Q-36,R-27..so, here (P) is in loss because (P) received 26 where it should have received 54..and (R) is in profit because it received 52 where it should have received 27..


$P$ gains the most i.e. 28, so the answer should be option (A).


Thank you, Charlie, for pointing it out, corrected it.


Charlie you dumb fuck! God damnit Charlie!


The question is wrong. It is 117, not 177.


Thank you for pointing out the typo, question has now been updated.


It is not 177, should be 117