Aptitude Discussion

Q. |
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? |

✔ A. |
$P$, Rs 28 |

✖ B. |
$Q$, Rs 35 |

✖ C. |
$R$, Rs 25 |

✖ D. |
$R$, Rs 27 |

**Solution:**

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.**

**Sid**

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**Deepak P S**

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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**

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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..

**Charlie**

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$P$ 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!

**Dinesh**

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

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

**P.Shekhar**

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It is not 177, should be 117

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