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?
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 3 of 12.
Nishant said:
1 decade ago
Ratio of times taken by A and B = 100:130 = 10:13.
A alone can do his piece of work in 23 days.
Let B takes x days to complete a given work.
A:B = 10:13.
23:B = 10:13.
B = 299:10.
A's 1 day work = 1:23.
B's 1 day work = 10:299.
(A+B) 's 1 day work = 1:23 + 10:299 = 1:13.
So, together they will complete the work in 13 days.
A alone can do his piece of work in 23 days.
Let B takes x days to complete a given work.
A:B = 10:13.
23:B = 10:13.
B = 299:10.
A's 1 day work = 1:23.
B's 1 day work = 10:299.
(A+B) 's 1 day work = 1:23 + 10:299 = 1:13.
So, together they will complete the work in 13 days.
Harish said:
1 decade ago
Had 100:130 confusion too due to misconception of "efficiency". See Physics says efficiency = (work of A/work of B) * 100. But here work is same, so we can use power. So E= (Power of A/Power of B) * 100. As work is same & P=W/T, so E = (time taken by B/time taken by A) * 100=130 So time taken by A:time taken by B :: 130:100.
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.
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.
Naseem Ahmad Saifi said:
10 years ago
A' s 1 day work =1/23......(1).
Now A is 30% faster of B.
So A's 1 day work = 130/100*B's 1 day work.
=> A = 13/10*B......(2).
From 1st and 2nd 13/10*B = 1/23 => B's 1 day work = 10/299......(3).
(A+B)'s 1 day work = 1/23+10/299 = 23/299.
So they complete work in 299/23 i.e. 13 days.
Now A is 30% faster of B.
So A's 1 day work = 130/100*B's 1 day work.
=> A = 13/10*B......(2).
From 1st and 2nd 13/10*B = 1/23 => B's 1 day work = 10/299......(3).
(A+B)'s 1 day work = 1/23+10/299 = 23/299.
So they complete work in 299/23 i.e. 13 days.
Sai kumar kaveti said:
9 years ago
A usually takes 23 days to finish the work and is 30% more efficient than B.
As per this,B should take = (130%) * (A) ------time to do work.
=> (130/100) * 23 => 1.3 * 23 ==> 29.9.
Now, (A + B) 1 day work = [1/23 - 1/29.9] = 1/13.
Therefore, A & B takes 13 days to finish the work.
As per this,B should take = (130%) * (A) ------time to do work.
=> (130/100) * 23 => 1.3 * 23 ==> 29.9.
Now, (A + B) 1 day work = [1/23 - 1/29.9] = 1/13.
Therefore, A & B takes 13 days to finish the work.
Sushruth said:
6 years ago
FROM : @Abhishek - A does the work in 23 days and he is 30% faster also, so B will do that work in (23+ 30% of 23)= 29.9 days.
Now work done in 1 day by A= (1/23) and B=(1/29.9),
work done by A+B in one day = (1/23 + 1/29.9) = 1/13,
So the workdone by A+B will be in 13 days.
Now work done in 1 day by A= (1/23) and B=(1/29.9),
work done by A+B in one day = (1/23 + 1/29.9) = 1/13,
So the workdone by A+B will be in 13 days.
(2)
Vivek said:
1 decade ago
A can do whole work in 23 days.
We have ratio 100:130 = 10(b):13(a).
A takes 23x13 to complete a work in 299 days.
Here 299 is total work which A alone can do in 23 days.
So we know total work is 299.
Both can take 10:13 = 23 days.
Total work/together work = 299/23 = 13.
We have ratio 100:130 = 10(b):13(a).
A takes 23x13 to complete a work in 299 days.
Here 299 is total work which A alone can do in 23 days.
So we know total work is 299.
Both can take 10:13 = 23 days.
Total work/together work = 299/23 = 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).
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).
Priti said:
1 decade ago
Say B does the work in x days.
A is 30% more efficient than B.
That means A will do it in x- (30*x/100) which is equal to 23 days.
So,
X-30*x/100=23.
70x=2300.
X=230/7.
So A and B together will work in.
[1/23+7/230]y=1.
Y=230/17=13.53=13 days (approx).
A is 30% more efficient than B.
That means A will do it in x- (30*x/100) which is equal to 23 days.
So,
X-30*x/100=23.
70x=2300.
X=230/7.
So A and B together will work in.
[1/23+7/230]y=1.
Y=230/17=13.53=13 days (approx).
Abhishek said:
6 years ago
A does the work in 23 days and he is 30% faster also, so B will do that work in (23+ 30% of 23)= 29.9 days.
Now work done in 1 day by A= (1/23) and B=(1/29.9),
work done by A+B in one day = (1/23 + 1/29.9) = 1/13,
So the workdone by A+B will be in 13 days.
Now work done in 1 day by A= (1/23) and B=(1/29.9),
work done by A+B in one day = (1/23 + 1/29.9) = 1/13,
So the workdone by A+B will be in 13 days.
(1)
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers