Aptitude - Time and Work

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).


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 produces x candles in 1 min.
5

II. gives, Machine X and Y produce x candles in 1 min.
2

From I and II, Y produces x - x = 3x candles in 1 min.
2 5 10

3x candles are produced by Y in 1 min.
10

x candles will be produced by Y in 10 x x min = 10 min.
3x 3

Thus, I and II both are necessary to get the answer.

Correct answer is (E).