Problems on Time and Work Part 3

Problems on Time and Work Part 3


Directions to Solve
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.
77
2work was carried by A.
7
II. is irrelevant.
 Correct answer is (A).
2. 
How long will Machine Y, working alone, take to produce x candles?
I. 
Machine X produces x candles in 5 minutes.
 II. 
Machine X and Machine Y working at the same time produce x candles in 2 minutes.
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 E
Explanation:
 I. gives, Machine X producesxcandles in 1 min.
5
II. gives, Machine X and Y producexcandles in 1 min.
2
From I and II, Y producesx-x=3xcandles in 1 min.
2510
3xcandles are produced by Y in 1 min.
10
x candles will be produced by Y in10xmin =10min.
3x3
Thus, I and II both are necessary to get the answer.
 Correct answer is (E).

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
1. 
In how many days can 10 women finish a work?
I. 
10 men can complete the work in 6 days.
II. 
10 men and 10 women together can complete the work in 33days
7
 III. 
If 10 men work for 3 days and thereafter 10 women replace them, the remaining work in completed in 4 days.
A.Any two of the three
B.I and II only
C.II and III only
D.I and III only
E.None of these
Answer: Option A
Explanation:
  I. (10 x 6) men can complete the work in 1 day.
       1 man's 1 day's work =1
60

 II.10 x24men +10 x24women can complete the work in 1 day.
77
      240men's 1 day work +240women's 1 day work = 1.
77
      240x1+240women's 1 day's work = 1.
7607
      240women's 1 day's work =1 -4=3
777
       10 women's 1 day's work =3x7x 10=1
72408
      So, 10 women can finish the work in 8 days.

III. (10 men's work for 3 days) + (10 women's work for 4 days) = 1
       (10 x 3) men's 1 day's work + (10 x 4) women's 1 day's work = 1
       30 men's 1 day's work + 40 women's 1 day's work = 1

      Thus, I and III will give us the answer.
      And, II and III will give us the answer.
       Correct answer is (A).

2. 
How many workers are required for completing the construction work in 10 days?
I. 
20% of the work can be completed by 8 workers in 8 days.
II. 
20 workers can complete the work in 16 days.
 III. 
One-eighth of the work can be completed by 8 workers in 5 days.
A.I only
B.II and III only
C.III only
D.I and III only
E.Any one of the three
Answer: Option E
Explanation:
  I.20work can be completed by (8 x 8) workers in 1 day.
100
   Whole work can be completed by (8 x 8 x 5) workers in 1 day.
        =8 x 8 x 5workers in 10 days = 32 workers in 10 days.
10

 II. (20 x 16) workers can finish it in 1 day.
  (20 x 16)workers can finish it in 10 days.
10
   32 workers can finish it in 10 days.

III.1work can be completed by (8 x 5) workers in 1 day.
8
   Whole work can be completed by (8 x 5 x 8) workers in 1 day.
        =8 x 5 x 8workers in 10 days = 32 workers in 10 days.
10
 Any one of the three gives the answer.
 Correct answer is (E).
Directions to Solve
Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.
1. 
8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work?
I. 
19 men and 12 women together can complete the work in 18 days.
II. 
16 men can complete two-third of the work in 16 days.
 III. 
In 1 day, the work done by three men in equal to the work done by four women.
A.I only
B.II only
C.III only
D.I or II or III
E.II or III only
Answer: Option D
Explanation:
Clearly, I only gives the answer.
Similarly, II only gives the answer.
And, III only gives the answer.
 Correct answer is (D).

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