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Aptitude Questions – Data Interpretation

I. Study the following graph carefully to answer the given questions

graph-time-and-work

  1. P and R started the work jointly. A few days later U also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.600. What is the Share of U?
    A. Rs.360
    B. Rs.385
    C. Rs.240
    D. can’t be determined
    E. None of these

    Answer & Explanation
    Answer – C. Rs.240
    Explanation :
    Efficiency of P = 4%
    Efficiency of R = 2%
    [(4+2)*10] = 60%
    The remaining work was done by U = 40%.
    40% of 600 = 240
  2. Q and S work together for 5 days, the rest of the work is finished by M in two more days. If they get Rs. 6000 as wages for the whole work, what are the daily wages of Q, S and M respectively?
    A. 200, 250, 300
    B. 300, 200, 250
    C. 600, 400, 200
    D. 600, 400, 500
    E. None of these

    Answer & Explanation
    Answer – D. 600, 400, 500
    Explanation :
    Explanation:
    Q’s 5 days work = 50%
    S’s 5 days work = 33.33%
    M’s 2 days work = 16.66% [100- (50+33.33)] Ratio of work of Q, S and M = 3: 2: 1
    Q’s total share = Rs. 3000
    S’s total share = Rs. 2000
    M’s total share = Rs. 1000
    Q’s one day’s wage = Rs.600
    S’s one day’s wage = Rs.400
    M’s one day’s wage = Rs.500
  3. The efficiency of L is 25% more than P. L started a work alone and then P joined her 5 days before actual completion of the work. For how many days L worked alone?
    A. 9
    B. 11
    C. 10
    D. 25
    E. 12

    Answer & Explanation
    Answer – B. 11
    Explanation :
    Efficiency (L : P) = 5 : 4
    Number of days(L : P) = 4x : 5x = 4x : 25
    ∴ Number of days required by L to finish the work alone = 4x
    = 4 x 5 = 20.
    L and P work together for last 5 days = 5 x 9 = 45%
    Efficiency of L = 5% and P’s efficiency = 4%
    ∴ No. of days taken by L to complete 55% work = 55/5 = 11days
  4. R started the work and left after some days, when 25% work was done. After it Z joined and completed it working for 25 days. In how many days R and Z can do the complete work, working together?
    A. 6
    B. 8
    C. 10
    D. 12
    E. 20

    Answer & Explanation
    Answer – E. 20
    Explanation :
    Efficiency of R = (100/50) = 2%
    Rest work = 75%
    ∴ Efficiency of Z = 75/25 = 3%
    ∴ Combined efficiency of R and Z = 5%
    ∴ Number of days required by R and Z to work together = 100/5 = 20 days.
  5. T and V started the work. After 3 days Z joined them, who can complete alone the same whole work in 3 days. What is the total number of days in which they had completed the work?
    A. 12
    B. 8
    C. 4
    D. 6
    E. None of these

    Answer & Explanation
    Answer – C.4 days
    Explanation :
    Efficiency of T and V = 11.11 + 5.55 = 16.66%
    Work done in 3 days = 3 x 16.66 = 50%
    Rest work done by T, V and Z = 50/50 = 1 day
    Work can be completed in 4 days.
  6. A is twice efficient as B and together they do the same work in as much time as T and V together. In how many days A can complete the work individually?
    A. 5 days
    B. 8 days
    C. 4 days
    D. 9 days
    E. None of these

    Answer & Explanation
    Answer – D. 9 days
    Explanation :
    1/x + 1/2x = 1/9 + 1/18
    3/2x = 3/18
    Number of days taken by A = 9 days
  7. After working for 3 days S is joined by O. If they complete the remaining work in 3 more days, in how many days can O alone complete the work?
    A. 10 days
    B. 8 days
    C. 5 days
    D. 12 days
    E. 15 days

    Answer & Explanation
    Answer – C. 5 days
    Explanation :
    Total days S worked = 3+3 = 6
    6/15 = 2/5
    So 3/5 = 3/x
    x = 5
  8. M can do a piece of work 5 days less than that of P. M and P began to work together but M leaves after some days and P completed the remaining work in 12 days. Number of days after which M left the job-
    A. 5.7/9 days
    B. 6.7/9 days
    C. 7.7/9 days
    D. 11.7/9 days
    E. None of these

    Answer & Explanation
    Answer – A. 5.7/9 days
    Explanation :
    (1/20 + 1/25)*T + 12/25 = 1
    We will get T = 52/9 i.e. 5.7/9 days
  9. X can do a certain work in the same time in which Y and R together can do it. If X and Y together could do it in the same time as that of Q then Y alone could do it in:
    A. 15 days
    B. 20 days
    C. 25 days
    D. 30 days
    E. 35 days

    Answer & Explanation
    Answer – C.25 days
    Explanation :
    X, Y and R’s 1 day work = 1/10 + 1/50 = 6/50 = 3/25
    X’s 1 day work = Y + R‘s 1 day work
    2*( x’s 1 day work) = 3/25
    x’s 1 day work = 3/50
    Y’s 1 day work = 1/10 – 3/50 = 2/50 = 1/25
  10. A can do a piece of work 10 days more than that of Q. Both of them start the work but A leaves the work 5 days before its completion. Find the time in which work is completed
    A. 10
    B. 15
    C. 20
    D. 25
    E. None of these

    Answer & Explanation
    Answer – A. 10
    Explanation :
    (1/10 + 1/20)*(T-5) + 5/20 = 1 (T is the number of days in which the work is completed)
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