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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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64.
Is it cheaper to employ X to do a certain job than to employ Y?
I. X is paid 20& more per hour than Y, but Y takes 2 hours longer to complete the job.
II. X is paid Rs. 80 per hour.
Answer & Solution
Answer: d)if the data even in both Statements I and II together are not sufficient to answer the question

Solution:   Suppose X takes x hours and Y takes (x + 2) hours to complete the job.

II. X is paid Rs. 80 per hour.
Total payment to X = Rs. (80x).

I. X = 120% of Y = (120/100) Y = (6/5)Y
=> Y = (5/6)X.

Y is paid Rs. [(5/6) * 80] per hour
=> Y is paid Rs. [(200/3)(x + 2)].

We cannot compare (80x) and 200/3(x + 2).

Correct answer is (d).
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Directions (Questions 65 to 68) : 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.
65.
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.
Answer & Solution
Answer: d) Any two of the three

Solution:   I. A can complete the job in 30 days.
A's 1 day's work = 1/30.
Remaining work = [1 - (5/7)] = 2/7

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

I and III also give the same answer.
II and III also give the same answer.

Correct answer is (d).
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66.
In how many days can the work be completed by A and B together? [Bank P.O. 2003]
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 alone can complete the work in 16 days.
Answer & Solution
Answer: b) Any two of the three

Solution:   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 work = [1/8 + 1/16] = 3/16.
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
=> 5/x = [1 - (3/8)] = 5/8.
=> x = 8.

(A + B)'s 1 day's work = [1/8 + 1/16] = 3/16.
Both can finish it in 16/3 days.

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

(A + B)'s 1 day's work = [1/8 + 1/16] = 3/16
Both can finish it in 16/3 days.

Hence, the correct answer is (b).
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67.
How many works are required for completing the construction work in 10 days? [Bank P.O. 2003]
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.
Answer & Solution
Answer: e) Any one of the three

Solution:   I. 20/100 work can be completed by (8 * 8) workers in 1 day.
Whole work can be completed by (8 * 8 * 5) workers in 1 day.
= (8 * 8 * 5)/10 workers in 10 days = 32 workers in 10 days

II. (20 * 16) workers can finish it in 1 day.
=> (20 * 16)/10 workers can finish it in 10 days.
=> 32 workers can finish it in 10 days.

III. 1/8 work can be completed by (8 * 5) workers in 1 day.
=> Whole work can be completed by (8 * 5 * 8) workers in 1 day.
= (8 * 5 * 8)/10 workers in 10 days = 32 workers in 10 days.

Any one of the three gives the answer.

Correct answer is (e) .
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68.
In how many days can 10 women finish a work? [R.B.I. 2002] I. 10 men can complete the work in 6 days.
II. 10 men and 10 women together can complete the work in 3 3/7 days.
III. If 10 men work for 3 days and thereafter 10 women replace them , the remaining work is completed in 4 days.
Answer & Solution
Answer: e) Any two of the three

Solution:   I. (10 * 6) men can complete the work in 1 day.
=> 1 man's 1 day's work = 1/60.

II. [10 * (24/7)] men + [10 * (24/7)] women can complete the work in 1 day.
=> (240/7) men's 1 day work + (240/7) women's 1 day work = 1.
=> [(240/7) * (1/60)] + (240/7) women's 1 day's work = 1.
=> (240/7) women's 1 day's work = [1 - (4/7)] = 3/7.
=> 10 women's 1 day's work = [(3/7) * (7/240) * 10] = 1/8.

So, 10 women can finish the work in 8 days.

III. (10 men's work for 3 day's) + (10 women's work for 4 days) = 1
=> (10 * 3) men's 1 day's work + (10 * 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 (e).
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Directions (Questions 69 to 70) : Each of the 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/are redundant and can be dispensed with while answering the given question.

69.
In how many days can the work be completed by A, B and C together? [S.B.I.P.O 2001]
I. A and B together can complete the work in 6 days.
II. B and C together can complete the work in 3     3/4 days
III. A and C together can complete the work in 3     1/3 days

Answer & Solution
Answer: (e) Information in all the three statements is necessary to answer the question.

Solution:   I. (A + B)'s 1 day's work = 1/6.
II. (B + C)'s 1 day's work = 4/15.
III. (A + C)'s 1 day's work = 3/10.

Adding, we get 2(A + B + C)'s 1 day's work = [1/6 + 4/15 + 3/10] = 22/30.
=> (A + B + C)'s 1 day's work = [(1/2) * (22/30)] = 11/30.

Thus, A, B and C together can finish the work in 30/11 days.

Correct answer is (e)
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70.
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? [S.B.I.P.O. 1999]
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 a day, the work done by three men is equal to the work done by four women.
Answer & Solution
Answer: d) I or II or III

Solution:   Clearly, I only gives the answer.
Similarly, II only gives the answer.
And, III only only gives the answer.

Correct answer is (d).
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