# Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 28)

28.

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

Answer: Option

Explanation:

Work done by X in 8 days = | 1 | x 8 | = | 1 | . | ||

40 | 5 |

Remaining work = | 1 - | 1 | = | 4 | . | ||

5 | 5 |

Now, | 4 | work is done by Y in 16 days. |

5 |

Whole work will be done by Y in | 16 x | 5 | = 20 days. | ||

4 |

X's 1 day's work = | 1 | , Y's 1 day's work = | 1 | . |

40 | 20 |

(X + Y)'s 1 day's work = | 1 | + | 1 | = | 3 | . | ||

40 | 20 | 40 |

Hence, X and Y will together complete the work in | 40 | = 13 | 1 | days. | ||

3 | 3 |

Discussion:

31 comments Page 2 of 4.
Prashant singh said:
5 years ago

How 3/40 is converted to 40/3?

Ashis said:
6 years ago

Thanks for the solution @Mohit.

Manu said:
7 years ago

The total work has done in two parts.

Y completed only 4/5 part of work. another part is done by X.

So work done by Y one day is 1/total work

= 5/4.

But, no need to get confused. simply solve as;

Y completed 4/5 part of work in 16 days.

one day's work is work/days.

divide 4/5 by 16.

We get the answer 1/20 directly.

Y completed only 4/5 part of work. another part is done by X.

So work done by Y one day is 1/total work

= 5/4.

But, no need to get confused. simply solve as;

Y completed 4/5 part of work in 16 days.

one day's work is work/days.

divide 4/5 by 16.

We get the answer 1/20 directly.

(2)

Mohit said:
8 years ago

First LCM of 40 is 40,

x can work 40 days,

work = 1 unit,

8*1 = 8,

remaining work 40 - 8 = 32,

Y finished it in 16 days then = 32/16 = 2,

x+y = 1+2 = 3,

40/3 answer.

x can work 40 days,

work = 1 unit,

8*1 = 8,

remaining work 40 - 8 = 32,

Y finished it in 16 days then = 32/16 = 2,

x+y = 1+2 = 3,

40/3 answer.

(2)

Pooka said:
8 years ago

Thank you @Parthasarathy.

P.muthukumar said:
8 years ago

What is the reason for converting 4/5 to 5/4?

Gobind Mandal said:
8 years ago

Why did you convert 4/5 to 5/4?

Makvana Disha said:
8 years ago

We are also do this,

x = 40days = 100%

For 8 days = ? (20%) so, 80% works remaining. That is done by y in 16 days.

80% = 16days

100% = ? (20days)

(x + y)'s 1 day work = (1/40) + (1/20).

= (3/40).

= (40/3) = 13*1/3.

x = 40days = 100%

For 8 days = ? (20%) so, 80% works remaining. That is done by y in 16 days.

80% = 16days

100% = ? (20days)

(x + y)'s 1 day work = (1/40) + (1/20).

= (3/40).

= (40/3) = 13*1/3.

Chetan said:
8 years ago

I am not sure about this answer but changing 4/5 to 5/4 could be because we are finding complete work for Y.

In other problems where same fractions were calculated, there we were finding remaining work. Here for Y, we are finding the Whole work. This could be the reason though I am not sure.

In other problems where same fractions were calculated, there we were finding remaining work. Here for Y, we are finding the Whole work. This could be the reason though I am not sure.

Scarlett said:
9 years ago

I still can't get the 4/5 converted to 5/4. In some of the previous sums it was not converted then why here?

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