Aptitude Discussion

Q. |
$A$ and $B$ undertake to do a piece of work for Rs 600. $A$ alone can do it in 6 days while $B$ alone can do it in 8 days. With the help of $C$, they can finish it in 3 days, Find the share of $C$? |

✖ A. |
70 |

✔ B. |
75 |

✖ C. |
80 |

✖ D. |
85 |

**Solution:**

Option(**B**) is correct

$C$’s one day’s work,

$= \left(\dfrac{1}{3}\right) - \left(\dfrac{1}{6}+\dfrac{1}{8}\right)$

$= \dfrac{1}{24}$

Therefore,

$A:B:C =$ Ratio of their one day’s work $

$= 1/6:1/8:1/24$

$= 4:3:1$

$A$’s share,

$= \text{Rs. }600×\dfrac{4}{8}$

$= 300$

$B$’s share,

$= \text{Rs. }600×\dfrac{3}{8}$

$= 225$

$C$’s share,

$= \text{Rs. } [600-(300+225)]$

$= \textbf{Rs. 75}$

**Edit:** For an alternative solution, check comment by **Sooraj.**

**Sooraj**

*()
*

A's one day work =1/6 of the work

B's one day work =1/8 of the work

Working together A, Band C they can complete it in 3 days i.e;

(A+B+C) one day work=1/3

1/6+1/8+C=1/3

C=1/3-(1/6+1/8)

C=1/24

Therefore C's one day work=1/24

Share of A for one day=600/6 //they undertook the work for 600//

=100

Then share of A for three days=3*100=300

Similarly

C's one day share =600/24=25

Then three days share =3*25=75 //As they work for 3 days//

A's work in a day =1/6 of the work

B's work in a day= 1/8 of the work

Work done by A and B together in a day =(1/6)+(1/8)=7/24

work done by A and B together in 3 days= (7/24)*3=7/8

Remaining work done by c=1-(7/8)=1/8

Share of C =600*(1/8)=75