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 13/4 times as efficient as B. The same job can be done by A alone in :

9 1 days
3

11 days

12 1 days
4

16 1 days
3

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

Therefore A's 1 day's work = ( 1 x 7 ) = 1 .
77 11

Discussion:
52 comments Page 1 of 6.

Menya Alex said:   2 years ago
Let A+B = 7 days.

Then (A+B)'s one day work = 1/7,
Let X represent B,
=> 7/4X + X = 1/7,
=>7X + 4X = 4/7,
=>11X = 4/7,
=>X = 4/77,
But A = 7/4X.
=> A = (7/4*4/77),
=> A = 1/11,
Giving us 11 days.
(8)

Lingaraj Behera said:   2 years ago
(A+B) 1day work is 1/7 --------------> (1)
Let 1-day work of A is 1/A, such as 1-day work of B is 1/B
Then 1/A + 1/B = 1A + 1/A * 7/4.

1/A + 4/7A = 11/7A--------------(2)
11/7A = 1/7,
7A = 77,
A = 11.
(4)

Sourav Kalal said:   3 years ago
Here is my simple approach
------------------------------------
A=7 (A's 1 day work)
B=4 (B's 1 day work)
------------------------------------
A+B = 11 (A+B's 1 day work).


A+B can finish work in 7 days,
So, Total work = 11*7=77 unit.

A can do 7 units of work in 1 day.

for 77 unit he will take 77/7= 11 days.
(7 ----> 1,
77 ---> ?) = 77/7.
(10)

Nesha said:   6 years ago
Thank you @Jimmy John.
(1)

Faisal said:   6 years ago
(A+B)'s 1 day = 1/7
And given that,
B=(4/7)A.

(A+ (4/7)A) 1 day = 1/7
(11/7) A 1 day = 1/7
11 A 1 day= 1
A's 1 day= 1/11.

Therefore, A needs 11 days alone to complete the required work.
(2)

Hellani said:   7 years ago
Can you please explain me? Please.
(1)

Prabhu said:   7 years ago
Nice explanation @Jimmy John.

Padma said:   7 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.

Padma said:   7 years ago
Why have they taken efficiency as such without converting it to number of days?

Swapna said:   7 years ago
7+4=11......28 ,7....? 11/7*28 = 44 ans.


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