Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 29)
29.
A and B can do a job together in 7 days. A is 1
times as efficient as B. The same job can be done by A alone in :
times as efficient as B. The same job can be done by A alone in :Answer: Option
Explanation:
| (A's 1 day's work) : (B's 1 day's work) = | 7 | : 1 = 7 : 4. |
| 4 |
Let A's and B's 1 day's work be 7x and 4x respectively.
| Then, 7x + 4x = | 1 |  11x = |
1 | x = |
1 | . |
| 7 | 7 | 77 |
 A's 1 day's work = |
 |
1 | x 7 |  |
= | 1 | . |
| 77 | 11 |
Discussion:
54 comments Page 2 of 6.
Padma said:
9 years ago
Efficiency of A:B = 7/4k : k.
No of days taken by A: B = 4k/7k = 4/7 (no of days taken = ratio of the reciprocals of the efficiency).
Let the work done in one day = 1/s.
then , work done by A in one day = 4/s.
work done by B in one day = 7/s.
work done by A+B = 1/7.
4/s + 7/s = 1/7.
11/s = 1/7.
s= 77.
Work done by A in one day = 4/s.
= 4/77.
the efficiency of A = 7/4.
Hence, work done by A in one day = 4/77 * 7/4.
= 1/11
Thus, A can do the job in 11 days.
No of days taken by A: B = 4k/7k = 4/7 (no of days taken = ratio of the reciprocals of the efficiency).
Let the work done in one day = 1/s.
then , work done by A in one day = 4/s.
work done by B in one day = 7/s.
work done by A+B = 1/7.
4/s + 7/s = 1/7.
11/s = 1/7.
s= 77.
Work done by A in one day = 4/s.
= 4/77.
the efficiency of A = 7/4.
Hence, work done by A in one day = 4/77 * 7/4.
= 1/11
Thus, A can do the job in 11 days.
(1)
Jimmy John said:
1 decade ago
A+B=1/7
7A+7B=1-----1
A=7/4B
4A=7B-----2
sub 2 in 1
7A+4A=1 (Since 7B=4A)
therefore 11A=1
A=1/11
therefore A can finish in 11 days
7A+7B=1-----1
A=7/4B
4A=7B-----2
sub 2 in 1
7A+4A=1 (Since 7B=4A)
therefore 11A=1
A=1/11
therefore A can finish in 11 days
(1)
Hellani said:
9 years ago
Can you please explain me? Please.
(1)
Nesha said:
8 years ago
Thank you @Jimmy John.
(1)
Yashwanth said:
9 years ago
What will be the answer for same problem with A is twice the efficiency of B?
Priya said:
1 decade ago
I didn't get why 7/4 is used?
Please explain.
Please explain.
Siri said:
1 decade ago
How you are getting 7/4? Anybody explain it please.
Juhi said:
1 decade ago
If 4/7 of a piece of work is completed in 7/4 days, in how many days can rest of the work be completed?
Kriti said:
1 decade ago
Guys I am not getting the concept of equation 1 and 2 please any one explain me in detail, please.
RAHUL ROY said:
1 decade ago
Step 1.
One day work of A and B, (A + B) = 1/7 ----> (1)
Step 2.
A:B =4:7, according to time not work.
Step 3.
Let assume A and B one day work be 1/4x and 1/7x.
Now, put the value of A and B in equation (1).
A + B = 1/4x + 1/7x.
=1/7 and getting x value as 11/4.
Step 4.
Put the value of x in A's 1-day work, 4x = 4X(11/4) =11.
One day work of A and B, (A + B) = 1/7 ----> (1)
Step 2.
A:B =4:7, according to time not work.
Step 3.
Let assume A and B one day work be 1/4x and 1/7x.
Now, put the value of A and B in equation (1).
A + B = 1/4x + 1/7x.
=1/7 and getting x value as 11/4.
Step 4.
Put the value of x in A's 1-day work, 4x = 4X(11/4) =11.
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