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 4 of 23.
Sagar Malunjkar said:
1 decade ago
@Surendra.
See carefully,
In second last step we have calculated C's 1days work is 5/48.
But our exact question is "C alone can do the job in how much days" so according to formula -
If C's 1 day's work = 1/n, then C can finish the work in n days ie n/1 days.
So that's why 5/48 became 48/5.
See carefully,
In second last step we have calculated C's 1days work is 5/48.
But our exact question is "C alone can do the job in how much days" so according to formula -
If C's 1 day's work = 1/n, then C can finish the work in n days ie n/1 days.
So that's why 5/48 became 48/5.
Anshu said:
1 decade ago
"A" can do the 1/16 of the work in a day.
"B" can do the 1/12 of the work in a day.
A + b + c = 1/4 of the work.
1/16 + 1/12 + c = 1/4.
3/48 + 4/ 48 + c = 1/4.
7/48 + c = 1/4.
C = 1/4 - 7/48 = 12-7/48 = 5/48.
C can do 5/48 of the work per day.
Therefore he can complete his work on 48/5 days = 9 3/5.
"B" can do the 1/12 of the work in a day.
A + b + c = 1/4 of the work.
1/16 + 1/12 + c = 1/4.
3/48 + 4/ 48 + c = 1/4.
7/48 + c = 1/4.
C = 1/4 - 7/48 = 12-7/48 = 5/48.
C can do 5/48 of the work per day.
Therefore he can complete his work on 48/5 days = 9 3/5.
Jeet said:
5 years ago
Take LCM of A and B.
The total work is 48.
A + B = 7 what should we add here so that work would complete in 4 days! So that number is 5.
3+4+5=12.
You can see they all can complete 48 works in 4 days. (48/12=4).
Therefore C's capacity is 5. When you'll divide the work by 5.
48/5 you'll get 9 3/5.
The total work is 48.
A + B = 7 what should we add here so that work would complete in 4 days! So that number is 5.
3+4+5=12.
You can see they all can complete 48 works in 4 days. (48/12=4).
Therefore C's capacity is 5. When you'll divide the work by 5.
48/5 you'll get 9 3/5.
Shirisha said:
6 years ago
@Sai Kumar.
It is 1÷16 + 1÷12 so 1st do LCM of 16,12 then you'll get the answer as 48 later on divide (48÷16, 48÷12) then you'll get answers as 3 and 4 (as multiplied by the numerator 1 then 3*1 will be 3 and 4*1 will be 4) add 3+4 you'll get 7 then the final answer will be 7/48
It is 1÷16 + 1÷12 so 1st do LCM of 16,12 then you'll get the answer as 48 later on divide (48÷16, 48÷12) then you'll get answers as 3 and 4 (as multiplied by the numerator 1 then 3*1 will be 3 and 4*1 will be 4) add 3+4 you'll get 7 then the final answer will be 7/48
Dumapti Mahesh said:
1 decade ago
I have another method to solve this:
Suppose the C's work take as z days.
We have the formula that (A+B+C) work = (xyz/(xy+yz+zx)).
Here x=12(A alone work),y=16(B alone work).
=>192z/(192+16z+12z)=4 days(given).
upon simplifying. we get,
48z = 192+28z.
z = 192/20=> 48/5.
Suppose the C's work take as z days.
We have the formula that (A+B+C) work = (xyz/(xy+yz+zx)).
Here x=12(A alone work),y=16(B alone work).
=>192z/(192+16z+12z)=4 days(given).
upon simplifying. we get,
48z = 192+28z.
z = 192/20=> 48/5.
Aparna said:
1 decade ago
@amit
First solve the bracket,
it is
(1/16+1/12)
First method:
Simply you can do cross multiplication
we get
(12+16)/12*16
after solving we get
7/48
Second method:
Find the lcm of denominators
that's of 12 and 16
It is 48,and multiply it with each fractions
i:e
we get
(3+4)/48
First solve the bracket,
it is
(1/16+1/12)
First method:
Simply you can do cross multiplication
we get
(12+16)/12*16
after solving we get
7/48
Second method:
Find the lcm of denominators
that's of 12 and 16
It is 48,and multiply it with each fractions
i:e
we get
(3+4)/48
Ishwar shrestha said:
9 years ago
Guys don't be confused.
A can do in 16 days.
B can do in 12 days.
A B & C can do in 4 days.
So,
Total work is to be done is 48.
( lcm of all)
Then A's efficiency is 3.
B's effc is 4.
A B n C effc is 12.
So, A + B + C = 12
4 + 3 + C = 12
7 + c = 12
C = 5.
Then 5/48 or 48/5.
A can do in 16 days.
B can do in 12 days.
A B & C can do in 4 days.
So,
Total work is to be done is 48.
( lcm of all)
Then A's efficiency is 3.
B's effc is 4.
A B n C effc is 12.
So, A + B + C = 12
4 + 3 + C = 12
7 + c = 12
C = 5.
Then 5/48 or 48/5.
Vamsi said:
1 decade ago
LCM of numbers 16, 12, 4 = 48.
16 is 3 times.
12 is 4 times.
4 is 12 times.
a-16d-3 units.
b-12d-4 units.
c-?- ? units.
a+b+c = 12 units .
Total work complete 12 units.
a+b complete 7.
Remaining work c 5.
= total/remaining work, 48/5 = 9.6 this is also written 9 3/5.
16 is 3 times.
12 is 4 times.
4 is 12 times.
a-16d-3 units.
b-12d-4 units.
c-?- ? units.
a+b+c = 12 units .
Total work complete 12 units.
a+b complete 7.
Remaining work c 5.
= total/remaining work, 48/5 = 9.6 this is also written 9 3/5.
Rahul Kapoor said:
2 years ago
A work done in 16 days.
B work done in 12 days.
A, B and C work done 4 days.
Total work 16,12,4.
Total work 48.
Efficiency of A 48/16 = 3
Efficiency of B 48/13 = 4
Efficiency of A+B+C = 48/4 = 12.
Efficiency of C = 12 - 4 - 3 = 5.
C completed the work alone =48/5.
B work done in 12 days.
A, B and C work done 4 days.
Total work 16,12,4.
Total work 48.
Efficiency of A 48/16 = 3
Efficiency of B 48/13 = 4
Efficiency of A+B+C = 48/4 = 12.
Efficiency of C = 12 - 4 - 3 = 5.
C completed the work alone =48/5.
(101)
Harmit said:
1 decade ago
Easiest method.
LCM is 48 of 16 &12. Then A can complete work in 3 work and B can 4 work.
Now A B C can complete 12 work.
Now A and B complete 7 work so still remaining work is 5.
So C can alone complete work 48/5. So answer is C. You can easily calculate.
LCM is 48 of 16 &12. Then A can complete work in 3 work and B can 4 work.
Now A B C can complete 12 work.
Now A and B complete 7 work so still remaining work is 5.
So C can alone complete work 48/5. So answer is C. You can easily calculate.
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