# 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:

32 comments Page 1 of 4.
Shushma Gulla said:
2 months ago

@All.

X - 40

X finished it in 8 days then 40 ÷ 8 = 5.

The efficiency of X is 1/5.

Total efficiency is 1, then Y = 1 - 1/5 = 4/5.

Y finished work in 16 days;

Y days efficiency is 5/4 (reciprocal of Y work efficiency).

Then Y =5/4×16 = 20.

X = 40, Y = 20.

Lcm is 40 (total work)

X is 1 unit, Y is 2 units

Together completed work X, Y is 40/3 = 13(1/3).

X - 40

X finished it in 8 days then 40 ÷ 8 = 5.

The efficiency of X is 1/5.

Total efficiency is 1, then Y = 1 - 1/5 = 4/5.

Y finished work in 16 days;

Y days efficiency is 5/4 (reciprocal of Y work efficiency).

Then Y =5/4×16 = 20.

X = 40, Y = 20.

Lcm is 40 (total work)

X is 1 unit, Y is 2 units

Together completed work X, Y is 40/3 = 13(1/3).

Anonymous said:
3 years ago

@All.

For those who are asking why 5/4 is multiplied,

Let's take an example, Suppose You complete work 1/2 of a work in 2 days. In how much time will you complete the entire work. 4 days right, how did you get it? you multiplied 2.

Eg:

1/2 : 2 is as 1: x, (I took 1 as it is the complete work).

Solving that, you still will get 4 as the answer. Same logic you can apply.

Thank you.

For those who are asking why 5/4 is multiplied,

Let's take an example, Suppose You complete work 1/2 of a work in 2 days. In how much time will you complete the entire work. 4 days right, how did you get it? you multiplied 2.

Eg:

1/2 : 2 is as 1: x, (I took 1 as it is the complete work).

Solving that, you still will get 4 as the answer. Same logic you can apply.

Thank you.

(3)

Ria Sharma said:
3 years ago

Thank you @Mohit.

Thiru said:
4 years ago

Take X's work as 1/40 he can do the work in only 8 days so 1/40*8=1/5.

Now 4/5 part of the work is remaining so Y is completing 4/5 part in 16 days 4/5 * 16 = 1/20.

Asking whole men's work1/20+1/40 = 13 1/3 days.

Now 4/5 part of the work is remaining so Y is completing 4/5 part in 16 days 4/5 * 16 = 1/20.

Asking whole men's work1/20+1/40 = 13 1/3 days.

Yeezuu said:
4 years ago

I am not getting the answer, Can anybody help? please.

(2)

Biswajit das said:
5 years ago

x in 40 days =100% work done.

Then in 08 days= 20 % work done.

The remaining work is 80 % which is done by Y in 16 Days.

in 16 Days =80 % work done.

Then in 20 Days =100 work done.

x=40.

y=20.

LCM =40 (Total work).

X one day work is 01 and 02 is Y's.

Then work done both x and y in= 40/3=13+1/3 Days.

Then in 08 days= 20 % work done.

The remaining work is 80 % which is done by Y in 16 Days.

in 16 Days =80 % work done.

Then in 20 Days =100 work done.

x=40.

y=20.

LCM =40 (Total work).

X one day work is 01 and 02 is Y's.

Then work done both x and y in= 40/3=13+1/3 Days.

(8)

Mir Adil said:
5 years ago

If x does a work at 8 days out of 40 days remaining 32 days are left.

Then y does remaining 32 days work in 16 days itself so Their ratio is 1:2 totally they can do 3 parts in one day, So 3+3+3+3+3+3+3+3+3+3+3+3+3 it completes 39 days here and 1/2 to complete 40 days.

Then y does remaining 32 days work in 16 days itself so Their ratio is 1:2 totally they can do 3 parts in one day, So 3+3+3+3+3+3+3+3+3+3+3+3+3 it completes 39 days here and 1/2 to complete 40 days.

(1)

Ganesh kumar said:
5 years ago

How 4/5 becomes into 5/4?

Please clarify it.

Please clarify it.

Midhun said:
6 years ago

Thanks @Manu.

(1)

Atul said:
6 years ago

Wonderful explanation, thanks @Mohit.

(1)

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