X takes 10 days to complete a task. Y takes half that time

Question

X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?

A. 2
B. 3
C. 4
D. 5
E. 6

A. 2
B. 3
C. 4
D. 5
E. 6

desaichinmay22 · Accepted Answer

Alone X takes 10 days to complete the task. Therefore rate of x=1/10
Y takes half the time to complete the task. Therefore Y's rate is double of X's rate=1/5

Let x be the total number of days A worked. Work=Rate*Days
40/100=1/10*x
x=4

Let y be the total number of days B worked. Work=Rate*Days
60/100=1/5*y
y=3

A worked for total 4 days and B worked for total 3 days. Hence both worked together for 3 days.
Ans=B

tass · Answer

So easy one I think................ cause Let they together done M days. and Y done 60% of the work.
So...... M/5=60/100......... M=3 days(simple)

Lucky2783 · Answer

if 40% is done by X , 60% is done by Y and question tells us clearly that Y joins X and they both continue together , X do not go anywhere once Y joined him, so the time it took Y to complete 60% of work will be the time both X and Y worked together.

5* 60% = 3 days

JeffTargetTestPrep · Answer

We can let the number of days X worked alone = x and the number of days X and Y worked together = t. Since the rate of X is 1/10 and the rate of Y is 1/5, we have:

x(1/10) + t(1/10) = 2/5

and

x(1/10) + t(1/10 + 1/5) = 1

If we subtract the first equation from the second, we have:

t(1/5) = 3/5
 
t = 3

Answer: B

pushpitkc · Answer

Since X takes 10 days to complete a task, Y must complete the task within 5 days
because Y takes half the time X takes to complete the work.

If the total unit of work is  50 units , X does  5 units/day  and Y does  10 units/day
 
We are told that 40% of the total work - 20 units is to be done by X.
Therefore, Y working along with X does 60% of the work - 30 units in  3 days(Option B)

Kinshook · Answer

Given: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. 
Asked: If 40% of the total work is done by X, for how many days did X and Y work together?

X takes 10 days to complete a task. 
Y takes 5 days to complete a task.

X starts working on the task and later Y joins X. Both work on the task together and complete the task. 
Let us assume that X worked for x days and then they both worked together for y days to complete the task

Work done by X = x/10 + y/10
Work done by Y = y/5
(x+y)10 + y/5 = 1
x/10 + 3y/10 = 1
x + 3y = 10

Work done by X = (x+y)/10 = .4
x + y = 4
X & Y worked together for = y = 3 days

IMO B

SVaidyaraman · Answer

Solution

Time actually worked by x = ax and by Y = ay
ax is also equal to ax1 + ax2 where ax1 is the time worked by x alone and ax2 time worked together and ax2=ay

ax/10+ay/5 = 1
(ax1/10 + ax2/10) +ay/5 =1
(ax1/10 +ay/10) +ay/5=1
ay/5 =1-4/10 = 6/10
ay=3

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X takes 10 days to complete a task. Y takes half that time

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X takes 10 days to complete a task. Y takes half that time

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