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 7 of 12.
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.
Dibakar said:
1 decade ago
See A alone can do the work in 23 days which is 30% less than B.
So that means B does the work in 23+0.3*23=29.9.
Now A+B together will take:
1/23+1/29.9 = 529/(23*299) = 1/13.
So it will take both of them 13 days :).
So that means B does the work in 23+0.3*23=29.9.
Now A+B together will take:
1/23+1/29.9 = 529/(23*299) = 1/13.
So it will take both of them 13 days :).
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.
Durga said:
10 years ago
Please explain shortcut method.
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.
Narayan said:
10 years ago
A = 30% of B.
Now 1 work two Man.
So, A + B = 1-------(1).
=> (30/100)B+B = 1.
=> 3B/10+B = 1.
=> 3B+10B = 10.
=> 13B = 10.
B = 10/13------(2).
(1) & (2) => A = 3/13.
Hence all total = 13 days.
Now 1 work two Man.
So, A + B = 1-------(1).
=> (30/100)B+B = 1.
=> 3B/10+B = 1.
=> 3B+10B = 10.
=> 13B = 10.
B = 10/13------(2).
(1) & (2) => A = 3/13.
Hence all total = 13 days.
Ramesh Naidu said:
10 years ago
Why can't we take 70% of 23 days? Then we get B's working days right?
But I'm not getting the same result why? Can you explain any one?
But I'm not getting the same result why? Can you explain any one?
Likhitha said:
9 years ago
A is 30% more efficient than B and A completes its work in 23 days.
100 : 23.
30 : ?.
That means for 30% 6.9 days.
A alone takes 23 days.
B alone takes 23 + 6.9 days (because B works 30% less efficient than A) = 29.9 days.
A and B together work for x days I. E.
x/23 + x/29.9 = 1(for easy calculation consider 29.9~30).
Hence, x = 13 days.
100 : 23.
30 : ?.
That means for 30% 6.9 days.
A alone takes 23 days.
B alone takes 23 + 6.9 days (because B works 30% less efficient than A) = 29.9 days.
A and B together work for x days I. E.
x/23 + x/29.9 = 1(for easy calculation consider 29.9~30).
Hence, x = 13 days.
Amit said:
9 years ago
We have to take 130:100? Why not 100:70?
Shada Akhtar said:
9 years ago
A = (130/100) *B (because A is 30% more efficient than B).
A =13B/10.
A =1/23 (Given).
1/23 = 13B/10.
B = 0/299.
A + B = 1/23 +10/299.
= 23/299 = 1/13.
Hence, both will take 13 days.
A =13B/10.
A =1/23 (Given).
1/23 = 13B/10.
B = 0/299.
A + B = 1/23 +10/299.
= 23/299 = 1/13.
Hence, both will take 13 days.
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