Data Sufficiency type questions are very common in almost all the sections of Quantitative Aptitude. This section checks the candidate’s concepts thoroughly about the topic and at the same time, it also checks the aptitude of the candidate. In the following section, we will see the work sufficiency type questions from the topic of Work and Time. Let us start.

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## Data Sufficiency – Work & Time

In these questions, you will be provided with directions. We will start with some solved examples and make ourselves more familiar with the concept of data sufficiency. Let us see below:

## Type I

#### Directions

(Questions 1 to 2): Each of the questions below consists of a statement and/or a question that follows with two statements i.e. I and II. Read both the statements and:

Write the 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 the 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.

Write the answer (c) if the data in Statement I or in Statement II alone are not sufficient to answer the question.

Give the answer (d) if the data even in both Statements I and II together are not sufficient to answer the question.

Write the answer (e) if the data in both Statements I and II together are necessary to answer the question.

### Solved Questions

Q 1. How long will Machine Y, working alone, take to produce x candles? [MBA 2002]

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.

Answer: I give, Machine X produces x/5 candles in 1 min. II gives, Machine X and Y produce x/2 candles in 1 min. From I and II, Y produces [x/2 – x/5] = 3x/10 candles in 1 min.

Therefore 3x/10 candles are produced by Y in 1 min. x candles are produced by Y in 1 min. x candles will be produced by Y in [10x/3x] min = 10/3 min. Thus, I and II both are necessary to get the answer. Therefore the correct option to select is (e).

Q 2: B alone can complete a work in 12 days. How many days will A, B, and C together take to complete the work?

I. A and B together can complete the work in 3 days.

II. B and C together can complete the work in 6 days.

Answer: Given: B’s one day’s work is equal to 1/12. The statement I gives, (A + B)’s 1 day’s work is equal to 1/3. This implies that A’s 1 day’s work = [1/3 – 1/12] = 3/12 = 1/4.

II gives, (B + C)’s one day’s work is equal to 1/6. This means that C’s 1 day’s work = [1/6 – 1/12] = 1/12.

Therefore (A + B + C)’s 1 day’s work = [1/4 + 1/12 + 1/12] = 5/12. Hence, they all finish the work in 12/5 = 2(2/5) days. Thus, I and II both are necessary to get the answer. Therefore the correct answer is (e).

### Type II

#### Directions

(Questions 1 to 2): Each of the following questions consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement(s) is/ are necessary to answer the question.

Q 1: In how many days can A and B working together complete a job?

I. A alone can complete the job in 30 days.

II. B alone can complete the job in 40 days.

III. B takes 10 days more than A to complete the job.

A) I and II only B) II and III only C) I and III only D) Any two of the three E) All I, II, and III.

Answer: I. A can complete the job in 30 days. Therefore A’s 1 day’s work = 1/30. Remaining work = [1 – 5/7] = 2/7.

II. B can complete the job in 40 days. Therefore B’s 1 day’s work = 1/40.

III. B takes 10 days more than A to complete the job. I and II gives, (A + B)’s 1 day’s work = [1/30 + 1/40] = 7/120. Therefore, I and II also give the same answer. II and III also give the same answer. Thus the correct answer is (D)

### Another Example

Q 2: In how many days can the work be completed by A and B together?

I. A alone can complete the work in 8 days.

II. If A alone works for 5 days and B alone works for 6 days, the work gets completed.

III. B lone can complete the work in 16 days.

A) I and II only B) II and III only

C) II and either I or III D) None of these E) Any two of the three [Bank P.O. 2003]

Answer: I. A can complete the job in 8 days. So, A’s 1 day’s work = 1/8.

II. A works for 5 days, B works for 6 days and the work is completed.

III. B can complete the job in 16 days. So, B’s 1 day’s work = 1/16. I and III: (A + B)’s 1 day’s = 1/16. I and III: (A + B)’s 1 day’s work = [1/8 + 1/16] = 3/16

Therefore both can finish the work in 16/3 days.

II and III: Suppose A takes x days to finish the work. Then, 5/x + 6/16 = 1. In other words, we can say that x = 8. Therefore, (A + B)’s 1 day’s work = [1/8 + 1/16] = 3/16. Thus both can finish it in 16/3 days.

I and II: A’s 1-day work = 1/8. Suppose B takes x days to finish the work. Then from II, [5×(1/8) + 6×(1/x)] = 1. Thus, 6/x = 3/8 and x = 16.

Therefore (A + B)’s 1 day work = [1/8 + 1/16] = 3/16. Thus both can finish the work in 16/3 days. Hence, the correct answer is (E).

## Practice Questions

Directions: Each of the following questions consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement(s) is/ are necessary to answer the question.

Q 1: 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. [Bank P.O. 2003]

Ans: E) Any one of the three.