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

I have edited the question to remove any ambiguity.

let the work be 100 units. since X takes 10 days to complete a task therefore x will do(100/10) 10 units per day and thus y will do 20 units per day.

therefore x and y 's combined 1 day work will be 10+20=30 units

now since y has completed 60% of the work by working with X, therefore x and y must have worked for 3 days.

hence answer should be B

Work rate of \(X = \frac{1}{10}\)

Work rate of Y\(= \frac{1}{5}\)

Combined rate \((X & Y) = \frac{1}{10} + \frac{1}{5} = \frac{3}{10}\)

Say X works alone for "a" days & (X + Y) work for "b" days

Work Done only by \(X = \frac{1}{10} . a\)

Total Work Done \(= \frac{1}{10} . a + \frac{3}{10} . b\)

\(= \frac{a + 3b}{10}\)

40% of Total work done = Work done by X

\(\frac{40}{100} \frac{(a + 3b)}{10} = \frac{a}{10}\)

a = 2b

I end up here....

Bunuel, can you kindly suggest next step........... or is the complete approach wrong?

Let me try to answer. The mistake is, Work done by x = (a + b)/10

You will then get b=3a. Substituting in the equations you will get b=3 which is the total number of days X and Y worked together.

I tried it; however not getting through

Equation comes up a follows:

\(\frac{40}{100} . \frac{a+4b}{10} = \frac{a+b}{10}\)

a = b

Hi,

There is an error. 40% of total work done is (40/100) (a+3b)/10 .Equate this to (a+b)/10. You will get the answer.

Let me try to answer. The mistake is, Work done by x = (a + b)/10

You will then get b=3a. Substituting in the equations you will get b=3 which is the total number of days X and Y worked together.[/quote]


I tried it; however not getting through

Equation comes up a follows:

\(\frac{40}{100} . \frac{a+4b}{10} = \frac{a+b}{10}\)

a = b[/quote]

Hi,

There is an error. 40% of total work done is (40/100) (a+3b)/10 .Equate this to (a+b)/10. You will get the answer.[/quote]


\(\frac{40}{100} \frac{a+3b}{10} = \frac{a+b}{10}\)

b = 3a

Answer = 3

Sravna: Thank you so much. Kudos to you
Now I'll retrospect as to why I failed to get the correct answer & how to avoid it in future

Dear Paresh,

You are welcome. If you know how the given info can be methodically used to arrive at the answer there is not a better way to solve the problem. It can come with practice or with guidance but it is something which can definitely be learnt. All the best.

The question is much eaiser solved by picking up a smart number. Let's say that Total Work = 100 (divisible by 10, 5 and 4).

The work rate of X = 10
The work rate of Y = 20 (as time is half of X, the rate is twice fatser)

X did some part of work in t days = 10t. The remaining work = 100-10t. X and Y completed the remaing work in [(100-10t) / 30] days. So

10t + 10 * [(100-10t)/30]*10=100*0.4
t=1
The remaining work 90. X and Y worked 90/30 = 3 days.

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)

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

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

t1 - days only when X worked
t2 - days when both X and Y worked together

Given: X's work => \(\frac{t1}{10}\) + \(\frac{t2}{10}\) = \(\frac{4}{10}\) => t1 + t2 = 4
Y's work => \(\frac{t2}{5}\) = \(\frac{3}{5}\) => t2 = 3 , so X and Y worked together for 3 days

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)

hi! can you please explain explain how does the work come out to be 3 days using this method since combined work rate is 15 units per day and remaining units are 30. Hence working together comes out to be 2 days?
Thanks!

let d=number of days X and Y work together
Y's rate=1/5
Y's share of total work=60%
1/5*d=.6
d=3
B

Overall X does 40% of the work and Y does 60 % of the work . IF there were 50 units of work in 10 days X would have completed 40% of 50 which is 20 units of work. Y would have done the remaining 30 units of work. Y would take 3 days to do that or in other words Y worked for 3 days which implies X and Y together worked for 3 days.