Aptitude Discussion

Q. |
Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. |

✖ A. |
Rs 40, Rs 60 and Rs 260 |

✔ B. |
Rs 36, Rs 81 and Rs 243 |

✖ C. |
Rs 42, Rs 86 and Rs 232 |

✖ D. |
Rs 38, Rs 88 and Rs 234 |

**Solution:**

Option(**B**) is correct

Assume there are 360 units of work (LCM of 90, 40 and 12).

Hence, A, B and C can do 4,9 and 30 units per day or together 43 units every 3 days.

So In 24 days, $43×8=344$ units of work is completed. In the next 2 days, 13 units are completed and on 27th day, C takes \(\left(\dfrac{1}{10}\right)^{th}\) of a day to finish the rest.

So, A and B worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by C.

The wages shall also be distributed in the same ratio as: **Rs 36, Rs 81 and Rs 243.**

**Edit:** A typo involving LCM has been corrected after it was pointed out by **Chirag Goyal.**

**Sidharth**

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**Sumit**

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How $A$ & $B$ worked for 9 days each?

Since 3 (A, B and C) people are working alternately for 24 days, so everybody is working for $\dfrac{23}{3}=8$ days.

Now work is still not complete and for the next two days, A an B respectively work on it to make progress in the job.

So they have worked for $8=1=9$ days in effect.

Hope this helps.

**Dan**

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couldn't understand this point :

" In 24 days, 43×8=344 units of work is completed.". We know that C worked only for 12 days. So we can't take it into account when calculating for 24 days right? Please explain me.

When $A,B$ and $C$ work for 3 days (1 day each) 43 units of work is completed so in 24 days $43\times \dfrac{24}{3}$ $=43 \times 8$ units of work will be completed.

And in these 24 days $C$ would have worked for $\dfrac{24}{3} \times 8$ days (so it dosen't reach 12 days limit).

**Chirag Goyal**

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Little mistake

Replace "Assume there are 360 units of work (LCM of 40, $60$ and 12)"

by this Assume there are 360 units of work (LCM of 40, $90$ and 12).

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

i don't understand why you have taken 24 days in above answer

as "So In 24 days, $43×8=344$ units of work is completed. In the next 2 days".