Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 17)
17.
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
11 days
13 days

20 3 days
17

None of these
Answer: Option
Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x     =>     x = ( 23 x 13 )     =>     x = 299 .
10 10

A's 1 day's work = 1 ;
23

B's 1 day's work = 10 .
299

(A + B)'s 1 day's work = ( 1 + 10 ) = 23 = 1 .
23 299 299 13

Therefore, A and B together can complete the work in 13 days.

Discussion:
119 comments Page 10 of 12.

Vishnuvardhan said:   8 years ago
As per the given data;

A = 130%B.
then
A = 130/100 B.
1/23 = 130/100 B. (as we know A=1/23)
B = 10/(13*23),
B = 10/299.

A and B together work is;
1/23 + 10/299,
23/299,
= 1/13.
Hence 13 days.

Ganesh said:   8 years ago
A is R% more than B, then B is less than A by.

(((R/(100+R)) * 100)%

Based on this formula,

We cant use A = 100% B = 70%.

Mannu said:   8 years ago
A alone takes 23 days to finish a job.

since A is 30% more efficient,
so B takes( A+30%(A) ) days,
i.e.,B takes ( 1.3*A = 1.3*23 ) days to complete it alone [ since A=23],
(A+B)'s one day work = ( 1/23 )+( 1/(1.3*23) ),
(A+B)'s one day work= 1/13.

Hence it takes 13 days for A alone to finish the work.

Radhika Sarraf said:   8 years ago
A takes 23 days to finish a work.

Since A is 30% more efficient than B, so obviously B will take 30% of time more than A to complete a work.

B=(A+30% of A),
=(23+(30/100)*23),
=(23+(69/10)),
=299/10.

So B takes 299/10 days to complete the work alone.

Now, A and B together 1 days work ((1/23)+(10/299)),
=1/13.
So both complete the work in 13 days.
HOPE THIS WILL HELP U TO UNDERSTAND THE PROBLEM IN A SIMPLE WAY.

Sandeep kumar said:   8 years ago
Total work= 299.
A+B= 13+10=23.

Total time= 299/23= 13.

ALLU said:   8 years ago
Efficiency and time are inversely proportional.
1/23 +1/(23*1.3)=1/x.
x = 13.

MAGGI said:   8 years ago
@Pallavi.

Ans: remaining amount f work is 1- 1/6 = 5/6.

5/6 is nothing but (1/6) 5. i.e 5 parts of 1/6.

In the question1/6 work takes 2 days and next part 50% faster.

We have 5 parts of 1/6 remaining (5/6) which is done in 5 days, each part of 1/6 takes 1 day (50% fast).

Riad said:   8 years ago
In 1 day, B can do x portion of the work.

So, A can do 1.3x portion of the work.

So, 1.3x=1/23..x=1/(23*1.3) portion of the work.. together in 1 day can do. (1/23+1/29.9)...Then in 13 day they can complete the whole work.

Siddharth said:   8 years ago
Answer is 10 people.
If a is 30% efficient than b. then,

Days ratio should be
a:b = 100:130, and a=1/23.

Solving this we get,
b = (13/230).
a+b = 10.

Bhishma said:   8 years ago
A is 30% effi then B.

So B=100%
A=130% take ratio=A/B=130/100=13:10
A:B
A, 13=1/23
B, 10=B cross xly
13B=10*1/23
B=10/23*13
B=10/299
A+B=1/23+10/299=1/13 days.


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