


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]
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:
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 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]
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. 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). 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). 