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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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57.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? [S.S.C. 2004]
Answer & Solution
Answer: b) Rs. 400

Solution:   C's 1 day's work = 1/3 - [1/6 + 1/8] = 1/3 - 7/24 = 1/24.

A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4 : 3 : 1

C's share = Rs. [(1/8) * 3200] = Rs. 400
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58.
A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for:
Answer & Solution
Answer: c) 12 days

Solution:   Let total money be Rs. x.

A's 1 day's wages = Rs. x/21.
B's 1 day's wages = Rs. x/28.

(A + B)'s 1 day's wages = Rs. [x/21 + x/28] = Rs. x/12.

Money is sufficient to pay the wages of both for 12 days.
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59.
A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Rs.1500 for the whole work, the daily wages of B and C are:
Answer & Solution
Answer: b) Rs. 225

Solution:   Part of the work done by A = [(1/10) * 5] = 1/2
Part of the work done by B = [(1/15) * 5] = 1/3
Part of the work done by C = 1 - [1/2 + 1/3] = 1/6.

So, (A's share) : (B's share) : (C's share) = 1/2 : 1/3 : 1/6 = 3 : 2 : 1.

A's share = Rs. [(3/6) * 1500] = Rs. 750
B's share = Rs. [(2/6) * 1500] = Rs. 500
C's share = Rs. [(1/6) * 1500] = Rs. 250

A's daily wages = Rs. (750/5) = Rs. 150
B's daily wages = Rs. (500/5) = Rs. 100
C's daily wages = Rs. (250/2) = Rs. 125

Daily wages of B and C = Rs. (100 + 125) = Rs. 225
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60.
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work? [R.R.B. 2003]
Answer & Solution
Answer: c) 15 days

Solution:   B's 1 day's work = [1/12 - 1/20] = 2/60 = 1/30.

Now, (A + B)'s 1 day's work = [1/20 + 1/60] = 4/60 = 1/15 {B works for half a day only}

So, A and B together will complete the work in 15 days.
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61.
A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in: [S.S.C. 2004]
Answer & Solution
Answer: d) 13    3/4 days

Solution:   (A + B)'s 2 day's work = [1/16 + 1/12] = 7/48.

Work done in 6 pair of days = [(7/48) * 6] = 7/8.
Remaining work = [1 - (7/8)] = 1/8.

Work done by A on 13th day = 1/16.
Remaining work = [1/8 - 1/16] = 1/16.

On 14th day, it is B's turn.
1/12 work is done by B in 1 day.
1/16 work is done by B in [12 * (1/16)] = 3/4 day.

Total time taken taken = 13   3/4 days.
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DATA SUFFICIENCY TYPE QUESTIONS
Directions (Questions 62 to 64) : Each of the questions given below consists of a statement and/or a question followed by two statements labelled I and II. Read both the 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 Statement I alone are not sufficient to answer the question;
Give answer (c) if the data either 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.

62.
How long will Machine Y, working alone, take to produce x candles? [M.B.A. 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 & Solution
Answer: (e) if the data in both Statements I and II together are necessary to answer the question.

Solution:   I gives, 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.

3x/10 candles are produces by Y in 1 min.
x candles will be produced by Y in [(10/3x) * x] min = 10/3 min.
Thus, I and II both are necessary to get the answer.

Correct answer is (e).
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63.
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 & Solution
Answer: (e) if the data in both Statements I and II together are necessary to answer the question.

Solution:   Given: B's 1 day's work = 1/12.

I gives, (A + B)'s 1 day's work = 1/3.
=> A's 1 day's work = [1/3 - 1/12] = 3/12 = 1/4.

II gives, (B + C)'s 1 day's work = 1/6.
=> C's 1 day's work = [1/6 - 1/12] = 1/12.

(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.

Correct answer is (e).
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