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SSC CPO Time and Work Quiz 6

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SSC CPO Time and Work Quiz 6

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SSC CPO Time and Work Quiz 6 is important for exams such as IBPS, RRB, SBI, IPPB, LIC AAO, GIC AO, UIIC AO, NICL AO, etc. SSC CPO Time and Work Quiz 6 will help you to learn more and more concepts in Time and Work. SSC CPO Time and Work Quiz 6 study plan is to utilize time and hard work towards smart work efficiently.

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1. A and B working together can complete a work in 12 days, B and C working together will complete the work in 15 days, C and A working together can complete the work in 20 days. If all three work together, in how many days the work can be completed?

    A. 10 days
    B. 8 days
    C. 13 days
    D. 12 days


Answer: Option: A

Explanation:
Given
A + B ‘s one day work will be \(\frac{1}{12}\)
Similarly, B + C’s one day work will be \(\frac{1}{15}\)
C + A ‘s one day work be \(\frac{1}{20}\)
A + B = \(\frac{1}{12}\) —-> (1)
B + C = \(\frac{1}{15}\) —-> (2)
C + A = \(\frac{1}{20}\) —-> (3)
Adding all the above equation we get
2(A+B+C) = \(\frac{1}{12}\) + \(\frac{1}{15}\) + \(\frac{1}{20}\)
=> \(\frac{5}{60}\) + \(\frac{4}{60}\) + \(\frac{3}{60}\)
=> \(\frac{12}{60}\)
A+B+C = \(\frac{12}{120}\)
= \(\frac{1}{10}\)
If all three work together, the work will be completed in 10 days.


2. Adam can do a job in 15 days, John can do the same job in 20 days. If they work together for 4 days on this job. What fraction of job is incomplete?

    A. \(\frac{1}{4}\)
    B. \(\frac{1}{10}\)
    C. \(\frac{7}{15}\)
    D. \(\frac{8}{15}\)


Answer: Option: D

Explanation:
Adam can do 1/15 of the job per day
John can do 1/20 of the job per day
If they work together they can do \(\frac{7}{60}\) of the work together
Remaining job 1 – 4*\(\frac{7}{60}\) = \(\frac{32}{60}\) = \(\frac{8}{15}\)


3. If A, B and C can do a job in 20, 30 and 60 days respectively. In how many days A can do the work if B and C help him on every third day?

    A. 12 days
    B. 15 days
    C. 16 days
    D. 18 days


Answer: Option: B

Explanation:

Efficiency of A = \(\frac{1}{20}\) = 5% per day
Efficiency of B = \(\frac{2}{30}\) = 3.33% per day
Efficiency of C = \(\frac{1}{60}\) = 1.66% per day
In three days A can do 15% of the job himself and B and C do 5% of the job ( 1.66% + 3.33% )
In three days they can do 20% of the job, to do 100% of the job, they need 3 × 5 = 15 days


4. Annie and David can complete the work in 28 and 84 days respectively. If they work together in how many days the work will get completed (in days) ?

    A. 21
    B. 42
    C. 63
    D. 20


Answer: Option: A

Explanation:
Given that Annie can do the work in 28 days which means Annie can complete 1/ 28th the work in 1 day
Given that David can do the work in 84 days which means David can complete 1/ 84th the work in 1 day
Let Annie one day work = \(\frac{1}{28}\)
Let David one day work = \(\frac{1}{84}\)
Both work together,
Together,they finish the work in \(\frac{XY}{X + Y}\) days
= \(\frac{( 28 × 84)}{(28 + 84)}\)
= \(\frac{2352}{112}\)
= 21 days.


5. Albert and Sam can complete a work in 12 and 36 days respectively. If both work together in how many days 50 % of the work will get completed?

    A. 4 days
    B. 5 days
    C. 4.5 days
    D. 5.5 days


Answer: Option: C

Explanation:
Let the time taken by Albert = A days = 12 days
the time taken by Sam = B days = 36 days
Albert + Sam together can complete 100 % of the work in:
=> \(\frac{1}{(A + B)}\) = \(\frac{1}{(A )}\)(1/A) + \(\frac{1}{(B)}\)
=> \(\frac{1}{(A + B)}\) = \(\frac{1}{(12)}\) + \(\frac{1}{(36)}\)
=> \(\frac{1}{(A + B)}\) = \(\frac{(36 + 12)}{((12 * 36)}\)
=> \(\frac{1}{(A + B)}\) = \(\frac{48}{432}\)
Taking reciprocal on both sides
A + B = \(\frac{432}{48}\)
A + B = 9 days
Thus 100% of the work is completed in 9 days,
50% of the work is completed in {(\(\frac{9}{100%}\)) * 50%} days = 4.5 days

1. Somu and Ramu can complete the work in 20 and 30 days respectively. In how many days, 50% of the work will get completed?

    A. 5
    B. 6
    C. 6.5
    D. 7.5


Answer: Option: B

Explanation:
Let the time taken by Somu= A = 20 days
the time taken by Ramu= B = 30 days
Then number of days to complete 100% of work by Somu+ Ramutogether:
=>\(\frac{1}{(A + B)}\) = (\(\frac{1}{a}\)) + (\(\frac{1}{b}\))
=> \(\frac{1}{(A + B)}\) = (\(\frac{1}{20}\)) + (\(\frac{1}{30}\))
=> \(\frac{1}{(A + B)}\) = (30 + 20) / (20 × 30)
=> \(\frac{1}{(A + B)}\) = \(\frac{50}{600}\)
Taking reciprocal on both sides
A + B = \(\frac{600}{50}\)
A + B = 12 days
Thus 100% of the work is completed in 12 days,
50% of the work is completed in {(\(\frac{12}{100%}\)) × 50%} days = 6 days


2. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

    A. 6 days
    B. 10 days
    C. 15 days
    D. 20 days


Answer: Option: B

Explanation:

X’s 1 day’s work = \(\frac{1}{20}\)
X’s 4 day’s work = \(\frac{1}{20}\) × 4 = \(\frac{1}{5}\)
The remaining work = \(\frac{4}{5}\)
X and Y’s 1 day work = \(\frac{1}{20}\) + \(\frac{1}{12}\) = \(\frac{4}{30}\) = \(\frac{2}{15}\)
Therefore, Both together finish the remaining work in \(\frac{4/5}{2/15}\) days
= \(\frac{4}{5}\)× \(\frac{15}{2}\) = 6 days
Therefore, the total number of days taken to finish the work = 4 + 6 = 10 days.


3. A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished he remaining work. In how many days A alone can finish the job?

    A. 40
    B. 50
    C. 55
    D. 60


Answer: Option: D

Explanation:
A + B ‘s 1 day’s work = \(\frac{1}{30}\)
Their 20 day’s work = \(\frac{1}{30}\) × 20 = \(\frac{2}{3}\)
Remaining work = \(\frac{1}{3}\)
\(\frac{1}{3}\) of the work is done by A in 20 days.
Then, whole work can be done by A in 3 × 20 = 60 days


4. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

    A. 30 days
    B. 40 days
    C. 60 days
    D. 70 days


Answer: Option: C

Explanation:
A + B’s 1 day’s work = 1/30
i.e. A + B = 1/30 ——— (i)
16 A + 44 B = 1 —— (ii) ( i.e. 1 = the whole work done)
Multiplying (i) by 16 and subtracting it from (ii), we get
i.e. 16 A + 44 B = 1
16 A + 16B = \(\frac{8}{15}\)
28 B = \(\frac{7}{15}\)
B = \(\frac{1}{60}\) i.e. B’s 1 day’s work = \(\frac{1}{60}\)
Therefore, B alone can finish the work in 60 days.


5. A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?


    A. 16
    B. 24
    C. 36
    D. 48


Answer: Option: B

Explanation:
According to the question,
A + B’s 1 day’s work = \(\frac{1}{12}\)
B+ C’s 1 days’ work = \(\frac{1}{16}\)
A worked for 5 days, B for 7 days and C for 13 days. So, we can assume that,
A+ B has been working for 5 days and B+ C has been working for 2 days and C alone for 11 days.
i.e. A’s 5 day’s work + B’s 7 day’s work + C’s 13 day’s work = 1
(A+ B)’s 5 days work + (B + C)’s 2 days work + C’s 11 day’s work = 1
\(\frac{5}{12}\) + \(\frac{2}{16}\) + C’s 11 days work = 1
So, C’s 11 day’s work = 1 – (\(\frac{5}{12}\) + \(\frac{2}{16}\)) = \(\frac{11}{24}\)
C’s 1 days’ work = \(\frac{11}{24}\) X \(\frac{1}{11}\) = \(\frac{1}{24}\)
Therefore, C alone can finish the work in 24 days.

1. A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was:

    A. 6
    B. 8
    C. 9
    D. 12


Answer: Option: C

Explanation:
A and B together can finish the work in 45 × 40/85 = \(\frac{360}{17}\) days
A and B’s 1 day’s work = \(\frac{17}{360}\)
A’s 1 day’s work = \(\frac{1}{45}\)
B’s 1 day’s work = \(\frac{1}{40}\)
B’s 23 day’s work \(\frac{1}{40}\) × 23 = \(\frac{23}{40}\)
Remaining work = 1 – 23/40 = \(\frac{17}{40}\)
\(\frac{17}{40}\) of the work is done by A and B together
\(\frac{17}{40}\) of the work is done by A and B together in = \(\frac{17}{40}\) X \(\frac{360}{17}\) = \(\frac{17}{40}\) × \(\frac{360}{17}\) days
= 9 days
Therefore, A left after 9 days.


2. A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in:

    A. 3 days
    B. 5 days
    C. 10 days
    D. 18 days


Answer: Option: B

Explanation:
A’ s 1 day’s work = \(\frac{1}{20}\)
B’s 1 day’s work = latex]\frac{1}{13}[/latex]
B’s 9 days work = latex]\frac{1}{12}[/latex] × 9 = \(\frac{3}{4}\)
Remaining work = latex]\frac{1}{4}[/latex]
A can finish the remaining work in = \(\frac{1}{4}\) X 20 = \(\frac{1}{4}\) ×20 = 5 days.


3. A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in

    A. 5 days
    B. 6 days
    C. 9 days
    D. 10 days


Answer: Option: B

Explanation:

A and B’s 1 day’s work = \(\frac{1}{3}\)
Their 2 day’s work = \(\frac{1}{3}\) × 2 = \(\frac{2}{3}\)
Remaining work = \(\frac{1}{3}\)
\(\frac{1}{3}\) of the work is finished by A in 2 days
Then, the whole work can be finished by A alone in 3 × 2 = 6 days
So, A’s 1 day’s work = \(\frac{1}{6}\)
Therefore, B’s 1 day’s work = \(\frac{1}{3}\) – \(\frac{1}{6}\) = \(\frac{1}{6}\)
Therefore, the whole work can be done B alone in 6 days


4. A man, a woman and a boy together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?

    A. 9 days
    B. 21 days
    C. 24 days
    D. 29 days


Answer: Option: A

Explanation:
Man + Boy + Woman)’s 1 day’s work = \(\frac{1}{3}\)
Man’s 1day’s work = \(\frac{1}{6}\)
Boy’s 1 day’s work = \(\frac{1}{18}\)
Then, Woman’ 1 day’s work = \(\frac{1}{3}\) – ( \(\frac{1}{6}\) + \(\frac{1}{18}\) ) = \(\frac{1}{3}\) – \(\frac{4}{18}\) = \(\frac{2}{18}\) = \(\frac{1}{9}\)
Therefore, the Woman alone can finish the work in 9 days


5. A and B together can complete a piece of work in 8 days while B and C together can do it in 12 days. All the three together can complete the work in 6 days. In how much time will A and C together complete the work?

    A. 8 days
    B. 10 days
    C. 12 days
    D. 20 days


Answer: Option: A

Explanation:
A’s 1 day’s work = A + B + C’s 1 day’s work – B + C’s 1 day’s work = \(\frac{1}{6}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)
B’s 1 day’s work = A + B’s 1 day’s work – A’s 1 day’s work = \(\frac{1}{8}\) – \(\frac{1}{12}\) = \(\frac{1}{24}\)
C’s 1 day’s work = B+ C’s 1 day’s work – B’s 1 day’s work = \(\frac{1}{12}\) – \(\frac{1}{24}\) = \(\frac{1}{24}\)
A +B’ 1 day’s work = \(\frac{1}{12}\) + \(\frac{1}{24}\) = \(\frac{3}{24}\)
Therefore, A and C together will finish the whole work in \(\frac{24}{3}\) = 8 days


Time and Work – Related Information
Time and Work Practice Quiz
Time and Work Practice Set 1
Time and Work Practice Set 2
IBPS RRB Time and Work Quiz Day 1