Latest Wipro Aptitude Question SOLUTION: Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both working together. If B worked alone, he would need 4 1/2 hours mor

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(#M40006427) WIPRO Numerical Ability question Time and work problems Keep an EYE

Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both working together. If B worked alone, he would need 4 1/2 hours more to compete the job than they both working together. What time would they take to do the work together.

Asked In Wipro (12 years ago)

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Read Solution (3) :

pawan kumar  (11 years ago)

let both are complete the work in x hour.
so, A complete the work in X+8 hour
B complete the work in X+9/2 hour
1/(X+8) + 1/(X+9/2) = 1/X
solve the equetion =2X^2=72
X^2=36
X=6.
so both can complete the work together in 6 days.

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Vaibhav Suresh Bhave  (8 years ago)

Let T be the number of hours to complete the job working together by A & B
Then T+8 = number of hours for A to complete the job working alone
and T+4.5 = number of hours for B to complete the job working alone

In 1 hour, A will complete 1 / ( T + 8 ) of the job
In 1 hour, B will complete 1 / ( T + 4.5 ) of the job
In 1 hour, A and B will complete 1 / T of the job

Then

1 / T = 1 / ( T + 8 ) + 1 / ( T + 4.5 ).......................................... ( 1 )
Then L.C .M = T ( T + 8 ) ( T + 4.5 )
Multiplying Eq ( 1 ) by the L C M
( T + 8 ) ( T + 4.5 ) = T ( T + 4.5 ) + T ( T + 8 )
T² + 8 T + 4.5 T + 36 = T² + 4.5 T + T² + 8 T
T² - T² - T² + 8 T + 4.5 T - 8 T - 4.5 T + 36 = 0
- T² + 36 = 0
36 = T²
6 =T = Time taken by both to complete the job = 6 hours

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ashish dhiman  (10 years ago)

Let us suppose both take x hours to complete the work

alone
A takes 8+x
B takes 9/2+x (by solving 4*1/2)

in 1 day
A 1/8+x
B (1/1)/(9/2+x/1) which becomes after solving 2/9+2x
B is 2/9+2x (1 day)
both(A+B) will take 1/x

Setting equation
(1/8+x)+(2/9+2x)=1/x (a+b=1/x) for 1 day
By applying rule for addition of such expressions on L.H.S.

((9+2x)(1)+(8+x)(2))/(8+x)(9+2x)=1/x

after solving

(4x+25)/(2x^2(i.e.raised to power of 2)+25x+72)=1/x
now cross multiply

x(4x+25)=2x^2+25x+72
solve it
2x^2=72
x^2=72/2 that is 36
x=square root of 36 i.e 6 Answer complete

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