Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 2)
2.
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Answer: Option
Explanation:
| (A + B + C)'s 1 day's work = | 1 | , |
| 4 |
| A's 1 day's work = | 1 | , |
| 16 |
| B's 1 day's work = | 1 | . |
| 12 |
 C's 1 day's work = |
1 | - |  |
1 | + | 1 |  |
= | |
1 | - | 7 | |
= | 5 | . |
| 4 | 16 | 12 | 4 | 48 | 48 |
| So, C alone can do the work in | 48 | = 9 | 3 | days. |
| 5 | 5 |
Discussion:
224 comments Page 3 of 23.
Ion Strait said:
2 years ago
The reason that 5/48 becomes 48/5 is that C's one day work = 5/48.
Here it means, the total work in units is 48 and out of that C does 5 units of work in 1 day, so it's 5/48.
But the question asks the time required for C alone to complete the work.
Since, 48 units are the total work, just divide it by the one-day unit of C's work, that is, 5
So, 48/5.
Here it means, the total work in units is 48 and out of that C does 5 units of work in 1 day, so it's 5/48.
But the question asks the time required for C alone to complete the work.
Since, 48 units are the total work, just divide it by the one-day unit of C's work, that is, 5
So, 48/5.
(50)
Abhishek said:
10 years ago
A - 16 days | 3 unit/day
L. C. M of (16, 12, 4).
| | = 48.
B - 12 days |4 unit/day|.
| |.
C - ? |x unit/day|.
-------------------------------------------------.
(A+B+C) - 4 days | 12 unit/day |.
So, for C we get (12-3+4) = 5 unit/day.
If C can do 5 unit in 1 day, then 48 unit can be done in 48/5 = 9*3/5 days.
Guys this is the easiest way.
L. C. M of (16, 12, 4).
| | = 48.
B - 12 days |4 unit/day|.
| |.
C - ? |x unit/day|.
-------------------------------------------------.
(A+B+C) - 4 days | 12 unit/day |.
So, for C we get (12-3+4) = 5 unit/day.
If C can do 5 unit in 1 day, then 48 unit can be done in 48/5 = 9*3/5 days.
Guys this is the easiest way.
Ammu said:
8 years ago
@Shruti.
A's one day work = 1/16.
B's one day work = 1/12.
with the help of C , they finished in 4 days.
So, A+B+C=4 days,
Therefore, (A+B+C)'s one day work = 1/4.
If C alone is = X.
then 1/16+1/12+X = 1/4,
X= 1/4-(1/16+1/12) {Lcm of 16, 12 is 48 and by the cross multiplication will get 7/48}
= 1/4-7/48,
= 12-7/48,
= 5/48,
C's one day work = 5/48.
A's one day work = 1/16.
B's one day work = 1/12.
with the help of C , they finished in 4 days.
So, A+B+C=4 days,
Therefore, (A+B+C)'s one day work = 1/4.
If C alone is = X.
then 1/16+1/12+X = 1/4,
X= 1/4-(1/16+1/12) {Lcm of 16, 12 is 48 and by the cross multiplication will get 7/48}
= 1/4-7/48,
= 12-7/48,
= 5/48,
C's one day work = 5/48.
Shakir said:
1 decade ago
We know a formula that,
If A do a work in X days, B do a work in Y days and C do a work in Z days.
Then all of three can do the same work in = XYZ/(XY+YZ+ZX).
Then,
According to question,
A do a work in 16 days,B do the same work in 12 days and let C do the same work in Days
Then we can write as,
(16*12*x)/(16*12+12x+16x) = 4.
And solve it.
If A do a work in X days, B do a work in Y days and C do a work in Z days.
Then all of three can do the same work in = XYZ/(XY+YZ+ZX).
Then,
According to question,
A do a work in 16 days,B do the same work in 12 days and let C do the same work in Days
Then we can write as,
(16*12*x)/(16*12+12x+16x) = 4.
And solve it.
Talib said:
4 years ago
A = 16.
B = 12.
A + B + C = 4.
Total work by a, b, c ie LCM of 16, 12, 4 = 48.
Then A work in 1 day = 48/16 = 3unit.
and B work in 1 day = 48/12 = 4 unit.
And A +B+C work in 1 days = 48/4= 12 unit.
Therefore put value of a and b ie 3 + 4 + c = 12.
ie c work in 1 day = 5 unit.
Therefore total work done by C is 48/5 ans simple and fast method.
B = 12.
A + B + C = 4.
Total work by a, b, c ie LCM of 16, 12, 4 = 48.
Then A work in 1 day = 48/16 = 3unit.
and B work in 1 day = 48/12 = 4 unit.
And A +B+C work in 1 days = 48/4= 12 unit.
Therefore put value of a and b ie 3 + 4 + c = 12.
ie c work in 1 day = 5 unit.
Therefore total work done by C is 48/5 ans simple and fast method.
(3)
Aparna said:
1 decade ago
@gurjit
as per formula,
If A's 1 day's work = 1/n , then A can finish the work in n days.
here also same
c's one days work=5/48
hence he can complete whole work in 48/5 days,tats asked to us
and remember any fraction can also be written in
quotient*remainder/divisor format
when solved 48/5
quotient=9
remainder=3
divisor=5
hence,
9*3/5
as per formula,
If A's 1 day's work = 1/n , then A can finish the work in n days.
here also same
c's one days work=5/48
hence he can complete whole work in 48/5 days,tats asked to us
and remember any fraction can also be written in
quotient*remainder/divisor format
when solved 48/5
quotient=9
remainder=3
divisor=5
hence,
9*3/5
Ritesh Raj said:
7 years ago
@All.
Check this;
A-16d
B-12d
C-xd.
Lcm of all 3=48x(let it be total work that they have to complete).
Now efficiency ( of A,B,C is 3x,4xand 48 resp)
Now. on 1st day all 3 together can do 3x+4x+48 works it is given that they together complete the work in 4 days so;
4*(3x+4x+48)=48 solve it get x, then you will get the answer.
Check this;
A-16d
B-12d
C-xd.
Lcm of all 3=48x(let it be total work that they have to complete).
Now efficiency ( of A,B,C is 3x,4xand 48 resp)
Now. on 1st day all 3 together can do 3x+4x+48 works it is given that they together complete the work in 4 days so;
4*(3x+4x+48)=48 solve it get x, then you will get the answer.
Palem Ganesh said:
5 years ago
It's quite easy, I will tell the shortcut method.
Take LCM of 16 an 12 is 48 and;
Then find one day work as units.
A = 48/16 = 4.
B = 48/12 = 3.
C = ?.
We know they all together they take just 4 days.
Per day of 4 days work = 48/4 = 12.
A + B + C = 12.
4 + 3 + C = 12.
C = 5.
So, C can do work 5 units per day.
C= 48/5.
Take LCM of 16 an 12 is 48 and;
Then find one day work as units.
A = 48/16 = 4.
B = 48/12 = 3.
C = ?.
We know they all together they take just 4 days.
Per day of 4 days work = 48/4 = 12.
A + B + C = 12.
4 + 3 + C = 12.
C = 5.
So, C can do work 5 units per day.
C= 48/5.
Sai kumar Reddy Nossam said:
7 years ago
common multiple for 12 and 16 is 48.
A's one day work =48/16=3 units,
B's one day work=48/12=4 units,
C's one day work??
A and B together do a piece of work in 4 days= 28 units.
remaining work ( C's work in 4 days)=48 - 20 =20 units,
C's work in one day=20/4=5 unit,
C alone can do the job in=(5 * 9)+3/5 = 9 3/5.
A's one day work =48/16=3 units,
B's one day work=48/12=4 units,
C's one day work??
A and B together do a piece of work in 4 days= 28 units.
remaining work ( C's work in 4 days)=48 - 20 =20 units,
C's work in one day=20/4=5 unit,
C alone can do the job in=(5 * 9)+3/5 = 9 3/5.
Soumya said:
1 decade ago
@Deepika.
C's 1 day work is 5/48.
Here we require C's total work.
Total work should be taken as '1'.
So, 1 day work i.e,5/48*number of days used to complete the work(unknown, so take it as 'x') = total work 1.
Simply, 5/48*x = 1.
5x = 48.
x = 48/5.
So C's total work is 48/5.
C's 1 day work is 5/48.
Here we require C's total work.
Total work should be taken as '1'.
So, 1 day work i.e,5/48*number of days used to complete the work(unknown, so take it as 'x') = total work 1.
Simply, 5/48*x = 1.
5x = 48.
x = 48/5.
So C's total work is 48/5.
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