Latest Gate Aptitude Question SOLUTION: If A is 20% less efficient than B. If B alone can do the work in 40 days. In how many days can A and B together complete the same work ? (a) 22 2/9 (b) 20 1/9 (c) 21 2/9 (d)

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(#M40038489) GATE Numerical Ability question Time and work Keep an EYE

If A is 20% less efficient than B. If B alone can do the work in 40 days. In how many days can A and B together complete the same work ?

(a) 22 2/9
(b) 20 1/9
(c) 21 2/9
(d) 32 2/9

Asked In Gate Suresh Kashyap (9 years ago)

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Swechchha Agarwal  (9 years ago)

B does 1/40 work in 1 day.
So, A will do 80% of 1/40 work, i.e., 1/50 work in 1 day.
Both together do (1/40 + 1/50 ), i.e., 9/200 work in 1 day.
So, time taken to complete work together will be 200/9 days, i.e., 22 2/9 days.

Option(a)

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Yamuna Muthusamy  (9 years ago)

Ratio of efficiency=80:100
ratio of times taken by A and B=100:80=5:4
A alone takes x days to do the job.
then,5:4::x:40
4x=40*5
x=50
A alone takes 50 days
1 day work when A and B works together =(1/50)*(1/46)
=9/200
A and B together complete the same work in 200/9 days=22 2/9 days

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sucheta  (9 years ago)

Ratio of time taken by A and B=120:100=6:5
Suppose A alone takes x days to do the job.
Then, 6:5::x:40 =>5x=6*40 =>x=48 days
(A+B)'s 1 day's work=1/48+1/40=11/240
A and B together complete the work in =240/11=21 9/11 days

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kaushik  (9 years ago)

suppose B is 100% efficient ,then A is 80%efficient
ratio of efficiencies of A and B is 80:100=4:5
ratio of times to complete work=5:4
B takes 40 days ,so 5:4=x:40(assuming A can do in x days)
=>200=4x
=>x=50
Now they together can complete the work in (1/50)+(1/40) =200/9 days

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Rahul Ranjan  (4 years ago)

Let us Suppose Efficiency of B is 100 then A is 80.
So Efficiency of A+B = 180
Work to be done A and b = 100 * 40 = 4000
Days to complete work by Both A + B = 4000 / 180 = 22 2/9 (a option )

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