# SSC CPO Time and Work Quiz 6

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# SSC CPO Time and Work Quiz 6

### Introduction

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.

### Quiz

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

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. $$\frac{8}{15}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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