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 2 of 12.
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.
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.
Aruna said:
9 years ago
Both can be solved using the same method.
T -25% more efficient than S =>.
For simple calculation let S be 100% efficient then T is 125%, so the time of work done ratio between T and S is T : S = 100 : 125 = 4 : 5.
Given S can do a piece of work in 20 days.
5 days of S = 4 days of T.
20 days of S= (4 * 20) /5 = 16 days.
The Same method can be used to solve the other one as well.
T -25% more efficient than S =>.
For simple calculation let S be 100% efficient then T is 125%, so the time of work done ratio between T and S is T : S = 100 : 125 = 4 : 5.
Given S can do a piece of work in 20 days.
5 days of S = 4 days of T.
20 days of S= (4 * 20) /5 = 16 days.
The Same method can be used to solve the other one as well.
Prathyusha said:
1 decade ago
It is given that A is 30% efficient than B,it means that A can do better WORK than B, so the time time taken by A will obviously be less than by B.
So, their ratio of times taken by A and B will get reversed. (As from the problem).The ratio of A and B work is 130:100, but the time taken by them to complete will get reversed that is 100:130.
Thank you!
CORRECT ME IF I AM WRONG PLEASE!
So, their ratio of times taken by A and B will get reversed. (As from the problem).The ratio of A and B work is 130:100, but the time taken by them to complete will get reversed that is 100:130.
Thank you!
CORRECT ME IF I AM WRONG PLEASE!
Shakti said:
1 decade ago
It's easy.
A work 30% more efficient than B.
A's efficiency = 1/23 word/day.......(1).
Let B's efficiency = x work/day.
Then A's efficiency(A/C to question) = x+x*(30/100) = 13x/10....(2).
From equation 1 & 2 we get x = 10/299.
So B's efficiency = 10/299 work/day.
Now, (A+B) efficiency = 1/23 +10/299 = 23/299 = 1/13 work/day.
So (A+B) will complete 1 work in 13 day(answer).
A work 30% more efficient than B.
A's efficiency = 1/23 word/day.......(1).
Let B's efficiency = x work/day.
Then A's efficiency(A/C to question) = x+x*(30/100) = 13x/10....(2).
From equation 1 & 2 we get x = 10/299.
So B's efficiency = 10/299 work/day.
Now, (A+B) efficiency = 1/23 +10/299 = 23/299 = 1/13 work/day.
So (A+B) will complete 1 work in 13 day(answer).
Bhargav said:
3 weeks ago
Let me assume supposed if A's efficiency is 100% then B's efficiency is 70%of A.
So,
Here given efficiency of A = 1/23
So B's efficiency is = 1/23(0.7),
= 7/230.
Now A+B work together;
So, 1/23+7/230.
= 17/230.
So the total no of days where A and B work together is 230/17.
Why isn't this answer is correct? plz, anyone explain.
So,
Here given efficiency of A = 1/23
So B's efficiency is = 1/23(0.7),
= 7/230.
Now A+B work together;
So, 1/23+7/230.
= 17/230.
So the total no of days where A and B work together is 230/17.
Why isn't this answer is correct? plz, anyone explain.
Soniya said:
9 years ago
A is 30% efficient than B so A = 130%of B.
Ratio of work done by A and B =130:100 = 13 : 10,
Then time taken by A & B will be 10 : 13.
Given that 10x = 23 days (A takes 23days to complete the work)
x = 23/10.
Whole work done (w) = work done by (A + B) = (1/10x ) + (1/13x) = 1/x * ((23/130)
= (10/23) * (23/130) = 1/13.
So, in 13 days A and B can complete the work.
Ratio of work done by A and B =130:100 = 13 : 10,
Then time taken by A & B will be 10 : 13.
Given that 10x = 23 days (A takes 23days to complete the work)
x = 23/10.
Whole work done (w) = work done by (A + B) = (1/10x ) + (1/13x) = 1/x * ((23/130)
= (10/23) * (23/130) = 1/13.
So, in 13 days A and B can complete the work.
Am average said:
7 years ago
A' 1day work =1/23,
A/c question,A is 30% more efficient than B.
i.e; A = 30% of B so;
1/23= 130/100 *B.
10/299=B 's 1-day work.
Note: when X % more is given, you have to take 100+x, if says X % less, then have to take
100-x.
So, (A +B ) 1 'days work = 1/23+10/229,
= 1/13.
Whole work to complete by A+B takes 13days.
A/c question,A is 30% more efficient than B.
i.e; A = 30% of B so;
1/23= 130/100 *B.
10/299=B 's 1-day work.
Note: when X % more is given, you have to take 100+x, if says X % less, then have to take
100-x.
So, (A +B ) 1 'days work = 1/23+10/229,
= 1/13.
Whole work to complete by A+B takes 13days.
Ravi kant yadav said:
9 years ago
Ais 30% more efficient than B.
Then their 1-day efficiency
A ----------B
130----------100
13---------- 10 (1-day work of A and B).
And total efficiency of A and B = 13 + 10 = 23
And time is taken by A and B together= A + B : A :: 23 : X.
(A + B)/A = 23/X (put the efficiency of A + B and A)
23/13 = 23/X (By solving it)
X = (23 * 13)/23 = 13days.
Then their 1-day efficiency
A ----------B
130----------100
13---------- 10 (1-day work of A and B).
And total efficiency of A and B = 13 + 10 = 23
And time is taken by A and B together= A + B : A :: 23 : X.
(A + B)/A = 23/X (put the efficiency of A + B and A)
23/13 = 23/X (By solving it)
X = (23 * 13)/23 = 13days.
Garima said:
9 years ago
Please, someone explain me the difference between the below question and the question asked in the above part.
Why different method followed to solve both but they look similar?
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
Here the Answer is 16.
Why different method followed to solve both but they look similar?
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
Here the Answer is 16.
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.
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