Latest TCS Aptitude Question SOLUTION: if A and B work together , they will complete a job in 7.5days.however, if A works alone and completes half of the work and then B takes over and complete the remaining half alone,

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if A and B work together , they will complete a job in 7.5days.however, if A works alone and completes half of the work and then B takes over and complete the remaining half alone, they will take 20days.how long will B alone takes to do the work if A is more efficient than B?

Asked In TCS ratna (11 years ago)

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Anurag  (11 years ago)

B will take 30 days
First of all,
(1/x)+(1/y)=1/7.5
and (x/2)+(y/2)=20
On solving,x=10,y=30
So,A tajes 10 days and B takes 30 days to complete the work

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karthick  (9 years ago)

Solution
A will complete (1/a) th of the job in a day.
B will complete (1/b) th of the job in a day.
A and B will complete the job in 7.5 or (15/2) days
(1/a) + (1/b) = 1 /(15/2)
(1/a) + (1/b) = 2/15 .......>1Eqn
From the question, we know that if A completes half the job working alone and
B takes over and completes the next half, they will take 20 days.
A can complete the job working alone in 'a' days,
so a/2 days
B will complete the remaining half of the job in days
so b/2 days
a/2 + b/2 =20
==> a+b=40 ==> a=40–b .....>2Eqn
sub eqn(2) in Eqn(1) we get
(1/40−b) + (1/b) = 2/15
(b + 40 - b)/ b(40-b) = 2/15
40/(40b-b^2) = 2 /15
600 = 80b- 2b^2
40-b^2 = 300 (Sub by 2)
B^2 - 40b + 300 = 0
(b−30)(b−10)=0
b=30 or b=10.
If b=30, then a=40−30=10
or
If b=10, then a=40−10=30.

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Nishant kumar  (5 years ago)

Let the total Work be 7.5
so, A+B unit time work= 1

Let A worked for x days then as per the question

(7.5/2)/x + (7.5/2)/(20-x)=1
(7.5/2)20=x(20-x)
x^2-20x+75=0
x=5,15
Since A more efficient so, B will take 15 days to complete half work or 30 days for whole work
30 Ans.

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