Matt and Peter can do together a piece of work in 20 days. After they

together, they can do a piece in 20 days, i.e. 1/m + 1/p = 1/20

In 12 days, they can finish 12*(1/20) = 3/5 of the piece. After Matt leaves, 2/5 still needs to be done by Peter, which he does in 10 days.

10/(2/5) = 25

Isn't this the same question? time-work-61136.html#p442431 But why do the answers differ...

Because Matt and Peter have some issues working together ..Just kidding.

Note that this problem is asking the the time taken by thr guy who did NOT stop working after 12 days while the question in link is asking the time taken by the guy who stopped working after 12 days.

Best way is this.
1) Get the unit of quantity of work. Make it a number which you find LCM of the given digits.
2) Calculate the rate of work for each person.
And then calculate what is asked.

So as per above,
Lets assume that 20*12=240 unit of work is there.
Assume rate of work per day for Matt is m, and for Peter is p;
so..
Matt and Peter can do together a piece of work in 20 days. implies..
(m+p)*20= 240
m+p=12
Now, peter works for 22 day while, matt works for 12 days.
so, 22p+12m=240
Solving the equations, we find the value of m and p as 2.4, and 9.6 unit of work/day respectively.
So peter will take, 240/9.6=25 days.

Work done by M&P in 12 days = 12/20 = 3/5

Remaining 2/5 is done by P alone in 10 days.

So P alone can do the entire work in (5/2) X 10 = 25 days

24.Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.
26days
27days
23days
25days
24 days

Rate Together * # of days working together + Rate of Peter * # of days working alone = 1 completed job

let P = 3 of hours Peter can complete one job alone

(1/20)*12 + (1/P)*10 = 1

P = 25

Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.

Peter completes the remaining (8/20) of the job in 10 days which means that the whole job(1) can be completed in X days.

<=> 8/20->10 <=> X=10/(8/20)= 25 Thus the answer is D.
1 -> X

To me, the most intuitive approach to solve work /rate problems is to use smart numbers.
Then we need to find the work rate - work done each entity in 1 day. The subsequent steps are then very easy .

If 2 entities A and B work together, then Work done by A in one day + Work Done by B in one day = Total work done by A and B in one day.
Example - If a machine produces 10 widgets per day and another machine produces 20 widgets per day, then working together both machines can produce 30 (10 + 20) widgets per day.

Let's choose a nr that is divisible by all the numbers given in the question stem - 20,12,10
LCM of 20,12,10 = 60
Let's assume that Total work = 60 units.
Matt and Peter work together to complete the work in 20 days. So the work done by both of them together is 3 units per day (60/20)
Now we are almost done

Matt and Peter worked together for 12 days. Hence working together, they completed 12 x 3 = 36 units of work
What remains is 24 units and Peter completed this work all by himself in 10 days
Hence peter's work rate = 24/10 units per day

Therefore, Time taken by peter to complete the 60 units of work = Total Work /Peter's work rate = (60)/(24/10) = 25 days

Matt and Peter together would complete 12/20=3/5th of the work in 12 days, thus the remaining 2/5th is done by Peter alone in 10 days.

Therefore Peter can complete the work alone in 10/(2/5)=25 days.

Answer: D.

\(\frac{1}{M}+\frac{1}{P}= \frac{1}{20}\)

Calculate work done together in 12 days:
\(\frac{1}{20}x12==>\frac{12}{20}=\frac{3}{5}\)

Remaining work is 1-3/5.
Calculate the days left for P to perform work alone:
\(\frac{1}{P}x10days=1-\frac{3}{5}\)
\(\frac{10}{P}=\frac{2}{5}\)
\(P=25 days\)


A. 26 days
B. 27 days
C. 23 days
D. 25 days
E. 24 days

let Matt & Peter be machines with efficiency m and p, so

m*p*20 = m*p*12 + p*10
m= (10/8)

Let Peter can complete in 10 days
m*p*20 = p*k
k=25

Bunuel is this approach correct, could you provide me with the repository of such sums.

We can let m and p be the number of days it takes Matt and Peter to complete the work independently and separately. So we have Matt’s rate = 1/m and Peter’s rate = 1/p. We can create the equations:

20(1/m + 1/p) = 1

and

12(1/m + 1/p) + 10(1/p) = 1

Dividing the first equation by 20, we have 1/m + 1/p = 1/20. Now, substituting 1/20 for (1/m + 1/p) in the second equation, we have:

12(1/20) + 10/p = 1

3/5 + 10/p = 1

10/p = 2/5

2p = 50

p = 25

Alternate Solution:

Since the job takes 20 days to complete by both of them working together, then in 12 days, 12/20 = 3/5 of the job is completed, and 1 - 3/5 = 2/5 of the job is left to be completed by Peter alone. We are given that Peter can complete 2/5 of the job in 10 days; therefore, Peter would complete 1/1 of the job in 10/(2/5) = 25 days.

Answer: D

They can complete the work in 20 days and hence they completed 12*1/20=3/5th of the work in 12 days

Work left = 1 - 3/5 =2/5

2/5th work is done by Peter alone in 10 days.

Rate of work completion by Peter=(2/5)/10 =1/25

So, Peter can complete the work alone in 25 days.
(option d)

D.S
GMAT SME

Let Work be 60 Units

Efficiency of M + P = 3 units/day

Work completed by them in 12 days will be 36 uinits ; 24 units work left

Now 24 units is completed by Peter in 10 days...

So, \(10p = 24\)

Or, \(p = 2.40\) units/day

So, The total job can be completed in 60/2.4 = 25 days, Answer must be (D)