Aptitude - Time and Work - Discussion

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

  • Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

1. 

A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the work was carried out by A?

I. 

A completed the job alone after A and B worked together for 5 days.

 II. 

Part of the work done by A could have been done by B and C together in 6 days.

[A]. I alone sufficient while II alone not sufficient to answer
[B]. II alone sufficient while I alone not sufficient to answer
[C]. Either I or II alone sufficient to answer
[D]. Both I and II are not sufficient to answer
[E]. Both I and II are necessary to answer

Answer: Option A

Explanation:

B's 1 day's work = 1
20

(A+ B)'s 1 day's work = 1
7

 I. (A + B)'s 5 day's work = 5
7

Remaining work = 1 - 5 = 2 .
7 7

2 work was carried by A.
7

II. is irrelevant.

Correct answer is (A).


Ankush said: (Jul 20, 2010)  
In this ques no doubt option A is correct, but I guess the explanation given is correct only if it's asked to find out part of work done by A alone.

But ques is wht part of work ws carried out by A(alone + A's contribution when both A & B worked together)which can be calculated as

B's 1 day's work = 1/20
(A+ B)'s 1 day's work = 1/7

=> A's 1 day's work = 1/7 - 1/20 = 13/140
=> A's 5 day's work = 13/28

Now , (A + B)'s 5 day's work = 5/7

Remaining work = 1 - 5/7 = 2/7

=> 2/7 work was carried by A alone

and

Total part of work carried by A = 2/7+13/28= 3/4.

Singh said: (Nov 1, 2010)  
Ankush you are genious yaar. You are 100% correct.

Deepa said: (Oct 27, 2011)  
Why we have calculated only for 5 days it may be 6 days too. ?

Javeed Ahmed Khan said: (Dec 16, 2011)  
Easy way of solving this question is:

A and B together can complete a task in 7 days which means

A+B = 7

B alone can do it in 20 days:

B=20

When we substitute B's Value we will get A's Value.

A+20=7
A=(13).

1st statement says that A will complete the task 5 days after A & B worked together, which is acceptable statement.

Munna said: (Dec 27, 2011)  
How we get 5/7 and 1-5/7=2/7 how it is possible tell me friend?

Lakshminarayana said: (Feb 23, 2016)  
Please explain deep I can't understand.

Srikanth said: (Mar 19, 2016)  
Could someone help me, how shall we get that 2/7 value.

2/7+1/7 results : 21/49 or 3/7 ?

Tunna said: (Jun 1, 2016)  
@Ankush.

Can you explain how you got the remaining work = 1 - 5/7 = 2/7 & A's 5days work= 13/28? How you got 28?

Akshay said: (Jun 20, 2016)  
@Ankush.

Agree with you, even I got the same answer.

Pihu said: (Aug 2, 2016)  
@Ankush.

How you got 28? please explain.

Sunilkumar said: (Sep 19, 2016)  
@Pihu.

A + B's 1day work = 1/7day.
B's 1day work = 1/20 day.
Then,
A + 1/20 = 1/7
After that,
A = 1/7 - 1/20.
by cross multiply,
A = 20 - 7\20 * 7.
A = 13\140.

Then we taking the I in that A completed the job alone after a&b worked together for 5 days.

So, 1st we take a can complete by 5 days.
Then A's 5days work = 13 * 5/140.
then we get 13/28.

Now we want to find A + B's 5days work.
A + B's 1day work = 1/7 day.
Then A + B's 5days work = 5/7 days.
Remaining work = 1 - 5/7 = 2/7 days.

Total part of work by A = 2/7 + 13/28
By taking Lcm = 2 * 4/7 * 4.

Then,
= 8/28 + 13/28 = 8 + 13/28.
After simplification we get,
= 21/28 = 3/4.

Vitthal Jadhav said: (Feb 12, 2017)  
B's 1 day's work = 1/20.
(A+ B)'s 1 day's work = 1/7.

=> (A + B)'s 5 day's work = 5/7.

Remaining work = 1 - 5 = 2.7 7
2/7work was carried by A.

Nabanita Biswas said: (Jun 29, 2017)  
From where we get 5?

Visithra. S said: (Jul 28, 2017)  
How "Remaining work =1-5" is done? Not understood please explain.

Manju P said: (Aug 10, 2017)  
How to find "x "when ((x÷15)+(5÷10))=1 is given.

Please tell me.

Nikhitha said: (Aug 19, 2017)  
@Manju.

Firstly given, x/15+5/10=1.
Where we get x/15=1-1/2.
On LCM we get, x/15=1/2.
Now, Cross multiply, 2x=15; x=15/2.

Bineeta said: (Dec 28, 2017)  
Why not E?

We required statement II also for solving the equation. Please explain me.

Shubham Nale said: (Jul 9, 2020)  
A+B takes 7 days to complete the whole work.
B takes 20 days.
Total work = LCM = 140,
A+B =20 unit/day.

For 5 days =100 unit work is done.
Therefore, 140-100 = 40 unit of work remained.
40/140 =2/7.

Keshri said: (Jul 22, 2020)  
It's easily understandable;
A+B=7.
B=20.
After substituting A's efficiency is 13.
So, 1 is agreed.

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