# 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 1 of 4.
SHEIK said:
1 decade ago

x can do work=1/40--->1

Let 8x+16y=1---->2(which is x &y can do work)

sub x value in above equ. we get

8(1/40)+16y=1

y=1/20.

finally, x=y will together=(1/40)+(1/20)=3/40

Hence, ans is (40/3)=13 1/3 days...

Let 8x+16y=1---->2(which is x &y can do work)

sub x value in above equ. we get

8(1/40)+16y=1

y=1/20.

finally, x=y will together=(1/40)+(1/20)=3/40

Hence, ans is (40/3)=13 1/3 days...

Bala said:
1 decade ago

Why you convert 4/5 into 5/4?

NARAYAN SAHOO said:
1 decade ago

x=40-8=32 ratio 2 capacity 1

y=16 ratio 1 capacity 2

Together done ration 3

Work is 40

Then 40/3

13.1/3

y=16 ratio 1 capacity 2

Together done ration 3

Work is 40

Then 40/3

13.1/3

Irshad said:
1 decade ago

Let x can do 1 work in a hour. Then he will do 8 work in 8 hour.

Remaining work = 40-8 = 32.

32/y=16;

y=2.

Means y do 1 work in 2hours.

x+y=3.

Together they will do in 40/3 day.

Remaining work = 40-8 = 32.

32/y=16;

y=2.

Means y do 1 work in 2hours.

x+y=3.

Together they will do in 40/3 day.

Student said:
1 decade ago

Can't get it because what does it mean of 16*5/4?

Sravani said:
1 decade ago

Ya we can't get. The remaining work of y is 4/5. But it taken has 5/4.

Heena roy said:
1 decade ago

X's 1 day work 1/40 ? how ?

Parthasarathy said:
1 decade ago

x's speed of work is 40, so work in 1 day is 1/40.

x does 8 days and leaves, so work done is 8*(1/40) = 1/5.

x does only 1/5 of the work , so remaining work to be done is 4/5 (1-1/5 = 4/5).

y's speed of work is not given, let us take it as 'K'. but he completes the remaining 4/5 work in 16 days.

So 16*(1/K)=4/5 which gives K = 20.

Now both together takes ( x speed of work + y speed of work).

1/40 + 1/20 = 3/40 = 1/(40/3) = 1/(13 1/3).

So the ans is 13 1/3.

x does 8 days and leaves, so work done is 8*(1/40) = 1/5.

x does only 1/5 of the work , so remaining work to be done is 4/5 (1-1/5 = 4/5).

y's speed of work is not given, let us take it as 'K'. but he completes the remaining 4/5 work in 16 days.

So 16*(1/K)=4/5 which gives K = 20.

Now both together takes ( x speed of work + y speed of work).

1/40 + 1/20 = 3/40 = 1/(40/3) = 1/(13 1/3).

So the ans is 13 1/3.

Keerthi said:
9 years ago

How to solve using LCM method?

Miftah said:
9 years ago

The main reason for 16*5/4 is unitary method. It goes like this:

It takes 4/5 work to completed by C = 16 days.

So for 1 work it will take: 16*5/4.

It takes 4/5 work to completed by C = 16 days.

So for 1 work it will take: 16*5/4.

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