When a duration of time (T) is required to complete a work (W) i.e. number of units of work done per unit time is called the rate of Work. Hence, Whenever some work is done and the total work itself can be taken as one unit.
Work: It is defined as the amount of job assigned or the amount of job actually done.
Time: Time is defined as the number of days or hours required to complete the task.
1. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
Options:
A. $\frac{1}{24}$ days
B. $\frac{7}{24}$ days
C. $3\frac{3}{7}$ days
D. $4$ days
Solution:
If A can do a piece of work in n days, then A's 1 day's work = $\frac{1}{n}$
(A + B + C)'s 1 day's work ==$\frac{1}{24} + \frac{1}{6} + \frac{1}{12} = \frac{7}{24}$
So, all the three together will complete the job in $=\frac{24}{7} = 3\frac{3}{7}$ days
Correct option: C
2.Mamta can alone complete a part of assignment in 8 days. Work done by Sunil alone in one day is half of the work done by Mamta alone in one day. In how many days can the assignment be completed, if Mamta and Sunil work together?
Options:
A. 5.33 days
B. 16 days
C. 24 days
D. 4 days
Solution:
Mamta can finish part of assignment in one day = $\frac{1}{8}$
Sunil can finish part of assignment in one day = $\frac{1}{16}$
Mamta + Sunil together finish part of assignment in one day = $\frac{1}{8} + \frac{1}{16} = \frac{3}{16}$
Therefore, together they will take$ \frac{16}{3}$
days = 5.33 days.
Correct option: A
3. A man M and woman W can do a work in 20 days together. The man can do the same job in 40 days alone. Then at what time the woman can complete the same work alone?
Options:
A. 10
B. 40
C. 30
D. 20
Solution:
W’s one day work = $\frac{1}{20}– \frac{1}{40}= \frac{1}{20}$
Therefore, she will take 20 days.
Correct Option: D
1. Madhab is twice as efficient as Minakhi. Madhab takes 30 days less than Minakhi to finish the work. Calculate the time required to finish the work together.
Options:
A. 40 days
B. 30 days
C. 20 days
D. 35 days
Solution:
Given Madhab is twice as fast as Minakhi
∴ if Madhab takes t days to complete the work
then Minakhi will take 2t days to complete same work
Given, 2a−a=30
⇒a=30
∴ Madhab takes 30 days and Minakhi takes 60 days to complete the same work
Say we have 60 units of work.
Then will do 1unit + 2unit of work respectively. ∴ To complete 60 units of work they would need $\frac{60}{3} = 20 $days ∴ Madhab & Minakhi together can complete a work in 20 days.Correct option: C
2. Riya can do a piece of work in 20 days. Madhu is 25% more efficient than Riya. The number of days taken by Madhu to do the same piece of work is:
Options:
A. 15 days
B. 16 days
B. 18 days
B. 25 days
Solution:
Ratio of times taken by Riya and Madhu = 125 : 100 = 5 : 4.
Suppose Madhu takes x days to do the work.
$5 : 4 :: 20 : x \implies x = \frac{4 \times 20}{5}$
$x = 16$ days
Hence, Madhu takes 16 days to complete the work.
Correct option: B
3.Rajesh takes 6 days to complete the assignment whereas Sita completes the same assignment in 12 days. In how much time they will complete the assignment together?
Options:
A. 2 days
B. 3 days
C. 4 days
D. 1 days
Solution:
Rajesh can do the same work in = 6 days
Sita can do the same work in = 12 days
Together they will do the work in $= \frac{1}{6} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4} = 4$ days
Correct Option: C
1. Three friends Akash, Bikah and Madhab can do a work together in 12, 18, and 24 days respectively. After working 4 days Akash and Madhab leaves the work. Find in how many days Bikah alone can complete the remaining work ?
Options:
A. $4\frac{18}{5}$ days
B. 10 days
C. 5 days
D. $\frac{18}{5}$ days
Solution:
(Akash + Bikah + Madhab)’s one day work = $\frac{1}{12} + \frac{1}{18}+ \frac{1}{24} = \frac{13}{72}$
4’s day work$ = 4 × \frac{13}{72} = \frac{13}{18}$
Therefore, remaining work $= 1 – \frac{13}{18} =\frac{5}{18}$
Now, time taken by Bikah to complete the work = $\frac{5}{18} = 5$
Correct option: C
2. Akash can complete a part of task in 25 days. His friend Dhawan can finish it in 18 days. They work together for 5 days and then Akash left the work. In how many days will Dhawan finish the remaining work?
Options:
A. 24 days
B. 25 days
C. 20 days
D. 11 days
Solution:
Time taken by Akash to finish the task = 25 days
Hence, Akash's one day work = $\frac{1}{25}$
Dhawan takes time to finish the work = 20 days
So, Dhawan's one day’s work = $\frac{1}{20}$
Akash + Dhawan's 1 day’s work = $\frac{1}{25} + \frac{1}{20} = \frac{9}{100}$
Akash + Dhawan's 5 day’s work = $5 × \frac{9}{100} = \frac{9}{20}$
Therefore, remaining work $(1 – \frac{9}{20} = \frac{11}{20}$
Now, $(\frac{11}{20})^{th}$ part of work is done by Dhawan in one day
Therefore, $\frac{11}{20}$work will be done by Dhawan in $20 × \frac{11}{20}$ = 11
Correct option: D
3. Mitali can finish his assignment in 18 days. His brother Manav can do the same assignment in 15 days. Manav worked for 10 days and left the assignment. In how many days, Mitali alone can finish the remaining assignment?
Options:
A. 4 days
B. 6 days
C. 10 days
D. 8 days
Solution:
Manav's one day work on assignment = $\frac{1}{15}× 10 = \frac{2}{3}$
Remaining work = $1 – \frac{2}{3}= \frac{1}{3}$
According to the question, A’s one day work =$ \frac{1}{18} $
Therefore $\frac{1}{3}$ work is done by Mitali in $\frac{1}{3} × 18 = 6$ days
Correct Option: B
1. A and B undertook a work for Rs. 4000. A alone can do a part of work in 6 days. B alone can do a part of work in 8 days. Their friend C joined them and they completed the work in 3 days. What is the share of C ?
Options:
A. Rs. 500
B. Rs. 800
C. Rs. 300
D. Rs. 120
Solution:
C's one day work $ = \frac{1}{3} – (\frac{1}{6} + \frac{1}{8} = \frac{1}{24}$
Their ratio of one day work $ = \frac{1}{6}: \frac{1}{8}: \frac{1}{24}$
C's worked for 3 days
Therefore, his share $ = 3 × \frac{1}{24} × 4000 = 500.$
Correct option: A
2. Maria can do a work in 10 days. James joined and they complete the same work in 8 days. If they get Rs. 100 for the work, what is the share of James?
Options:
A. Rs. 70
B. Rs. 20
C. Rs. 60
D. Rs. 40
Solution:
Maria can do the work in = 10 days
both can do the work in = 8 days
James can do the work = $\frac{1}{8} –\frac{1}{10}= \frac{5-1}{40} = \frac{1}{40} = 40 days$
Maria and James's share = 40: 10 = 4: 1
Therefore, James's share $= \frac{1}{5} × 100 x 1 = Rs. 20$
Correct option: B
3.Animesh, Sanvi, and Mad contracted a work for Rs. 10000. Together, Animesh and Sanvi completed $ \frac{6}{10}$ of the work. How much does Mad get ?
Options:
A. Rs. 4000
B. Rs. 5000
C. Rs. 4200
D. Rs. 4500
Solution:
Animesh + Sanvi did = $\frac{6}{10}$
Mad completed = $1 – \frac{6}{10} = \frac{4}{10}$
Animesh + Sanvi' share : Mad's share = 6 : 4
Mad's share = $\frac{4}{10}× 10000 = 4000.$
Correct Option: A