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.
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.
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).
Adithi said:
1 decade ago
A=1/23.
A=1.3B.
So B=1/(23*130/100).
B=10/(23*13).
A+B=1/23+1/(10/(23*13)).
So A+B=1/13.
Answer is 13 days.
A=1.3B.
So B=1/(23*130/100).
B=10/(23*13).
A+B=1/23+1/(10/(23*13)).
So A+B=1/13.
Answer is 13 days.
Deepak said:
1 decade ago
WORKING DAYS FOR A = 23 DAYS,
IN ONE DAY A = 1/23,
Since A 30% efficient ,WORKING DAYS FOR B=23+23*30/100=299/10 DAYS.
IN ONE DAY B = 1/(299/10)=10/299.
(A+B)*DAY = 1.
(1/23+10/299)*DAY = 1.
DAY = 299/23 = 13 DAYS.
IN ONE DAY A = 1/23,
Since A 30% efficient ,WORKING DAYS FOR B=23+23*30/100=299/10 DAYS.
IN ONE DAY B = 1/(299/10)=10/299.
(A+B)*DAY = 1.
(1/23+10/299)*DAY = 1.
DAY = 299/23 = 13 DAYS.
SK.Gopinath siva said:
1 decade ago
For those who stuck in solving the final step.
= 1/23 + 10/299.
= 1/23 (1/1 +10/13).
= 1/23 (13+10/13).
= 1/23 (23/13) =23/299 = 1/13 = 13.
= 1/23 + 10/299.
= 1/23 (1/1 +10/13).
= 1/23 (13+10/13).
= 1/23 (23/13) =23/299 = 1/13 = 13.
Sreepadh Reddy said:
1 decade ago
I got the answer as 10 days.
a:b = 130:100 as a is 30% more efficient than b.
So a:b = 130:100.
From which we get,
130:100::23:x.
a's work is = 1/23;
b's work is = 13/230.
a+b = 1/23+13/230 = 10.
a:b = 130:100 as a is 30% more efficient than b.
So a:b = 130:100.
From which we get,
130:100::23:x.
a's work is = 1/23;
b's work is = 13/230.
a+b = 1/23+13/230 = 10.
Ravi said:
1 decade ago
@Sk Gopinath Siva.
I don't get the way you added those fractions so could you please explain little bit more clear?
I don't get the way you added those fractions so could you please explain little bit more clear?
Srujan said:
1 decade ago
Here we assume A=130, and B=100.
We have noticed that A's one day work ((130)%) is 1/23.
B'S one day work ((100)%) is ?
Therefore, we get B's one day work as(100*(1/23))/130) = 10/((13)*23).
A+B one day's work is 1/23 + 10/(23*13) = 1/13.
We have noticed that A's one day work ((130)%) is 1/23.
B'S one day work ((100)%) is ?
Therefore, we get B's one day work as(100*(1/23))/130) = 10/((13)*23).
A+B one day's work is 1/23 + 10/(23*13) = 1/13.
Anshuman said:
1 decade ago
We have to solve this in this way also since A is 30 % more efficient than B it means.
A = B+B*3/100 i.e. A = 1.3B.
A = B+B*3/100 i.e. A = 1.3B.
Javid mir said:
1 decade ago
A = 23 days.
B = 30%more than A i.e, B=130% of A.
B = 130/100*23 = 299/10.
Now, A's 1 day work = 1/23.
B's 1 day work = 10/299.
Therefore, (A+B) completes 1 days work in (t)=1/23 + 10/299.
Solving for (t) we get, t=1/13.
t=13.
B = 30%more than A i.e, B=130% of A.
B = 130/100*23 = 299/10.
Now, A's 1 day work = 1/23.
B's 1 day work = 10/299.
Therefore, (A+B) completes 1 days work in (t)=1/23 + 10/299.
Solving for (t) we get, t=1/13.
t=13.
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