Answer: Option B
Explanation: Let the required number of days = x days
So, 150x (20x)30 = 2820
x=19 days
2. In the beginning, Ram works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Ram is to finish this work at a stretch, how many hours will he take to finish this work?
Answer: Option E
Explanation: Ram’s 16 hr work = \(\frac{16}{24}\) =\(\frac{60 × 70}{(60 + 70)}\). Remaining work = 1 – \(\frac{2}{3}\) = \(\frac{1}{3}\).
Using work and time formula: This will be completed in \(\frac{2}{3}\) × 18 i.e. 6 hrs.
So, total time taken to complete work = 16 + 6= 22 hrs.
3. A can do a piece of work in 10 days, and B can do the same work in 20 days. With the help of C, they finished the work in 4 days. C can do the work in how many days, working alone?
Answer: Option A
Explanation: Their combined 4 day work = 4(\(\frac{1}{10}\) + \(\frac{1}{15}\)) = \(\frac{12}{20}\) = \(\frac{3}{5}\).
Remaining work = 1 – \(\frac{3}{5}\) = \(\frac{2}{5}\).
This means C did \(\frac{2}{5}\) work in 4 days, hence he can finish the complete work in \(\frac{5}{2}\) × 4 = 10 days.
4. Ajay and Vijay undertake to do a piece of work for Rs. 480. Ajay alone can do it in 75 days while Vijay alone can do it in 40 days. With the help of Pradeep, they finish the work in 25 days. How much should Pradeep get for his work?
Answer: Option B
Explanation: In 24 days, they would have done \(\frac{1}{3}\) and \(\frac{5}{8}\) of the work.
The remaining work is 1 – (\(\frac{1}{3}\) + \(\frac{5}{8}\)) = \(\frac{1}{24}\).
This means Pradeep has done \(\frac{1}{24}\)th of the work, so he should be paid \(\frac{1}{24}\)th of the amount i.e. 480 × \(\frac{1}{24}\) = Rs. 20 is the answer.
5. Daku and Tamatar can do a piece of work in 70 and 60 days respectively. They began the work together, but Daku leaves after some days and Tamatar finished the remaining work in 47 days. After how many days did Daku leave?
Answer: Option E
Explanation: Tamatar would have done \(\frac{47}{60}\) work in 47 days. The remaining work i.e. \(\frac{13}{60}\) must have been done by Daku and Tamatar together. They can do the whole work in \(\frac{60 × 70}{(60 + 70)}\) = 60 × \(\frac{70}{130}\) = \(\frac{420}{13}\) days.
So, they would have done \(\frac{13}{60}\) work in \(\frac{420}{13}\) × \(\frac{13}{60}\) = 7 days. Therefore, Daku left work after 7 days.
Answer: Option E
Explanation: 100 * 10 days = 1000
Now 1000/200 = 5 days (Initial total no. of men engaged in the project)
Hence, 5 more days required to finish the work if 100 more men would not joined
2. A woman has her three daughters. First and second can take 24 and 30 days resp. to complete a work. In how many days third one takes to complete the work. If woman can complete the whole work alone in 3(3/11) days. The efficiency of woman is double than her three daughters.
Answer: Option B
Explanation: LCM = 72 (if we are taking woman and her two daughters )
Here it is given
Woman Three daughters
Time taken = 1 : 2
Efficiency= 2 : 1Three daughters, let P+Q+R = 11
3+2+R = 11
R=6 days
Her third daughter complete the work in = \(\frac{72}{6}\)= 12 Days
3. Ramesh and Ram can do a piece of work in 24 and 30 days respectively. They both started and worked for 6 days. Ram then leaves the work and another their friend Rohit joins the work and completed the remaining work with Ramesh in 11 days. Find how many days are taken by Rohit alone to finish the work
Answer: Option D
Explanation: (\(\frac{1}{24}\) + \(\frac{1}{30}\)) *6 +(\(\frac{1}{24}\) + \(\frac{1}{Rohit}\) ) *11 = 1
Therefore, Rohit takes 120 days to finish the work
4. A printer A can print one thousand books in 15 hours ,printer B can print the same number of books in 10 hours and printer C can print the same number of books in 12 hours . If all the printers are started to print the books at 8 A.M, After sometime printer A is closed at 9 A.M and printer B and printer C remains working. Find at what time the printing will be completed?
Answer: Option C
Explanation: Let printing completed in be T hours
Then A ‘s 1 hour work, B’s T hours work and C;s T hours work =Total work
\(\frac{1}{15}\) +\(\frac{T}{10}\)+\(\frac{T}{12}\) =1
T= 5(\(\frac{1}{11}\))
Hence, the printing of books will be completed at 5(\(\frac{1}{11}\))hours
5. A group of men decided to do a job in 4 days but 20 men dropped out everyday, the job was completed at the end of the 7th day. Find the men who are in the work initially?
Answer: Option D
Explanation: Total work = M * 4 = 4M
M + (M+20) +…….
\(\frac{7}{2}\) [2M +6(20)] = 4M
M=140
Answer: Option B
2. 12 Men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take to reap it?
Answer: Option D
Explanation: 12 men = 18 women or 1 man = \(\frac{3}{2}\) women
Therefore 8 men + 16 women = (8 × \(\frac{3}{2}\) + 16) women i.e.., 28 women
Now 18 women can reap the field in 14 days
Therefore, 28 women can reap it in = 9 days
3. 8 Children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by man to finish the work. In how many days will 12 men finish the same work?
Answer: Option D
Explanation: 2 children = 1 man
Therefore (8 children +12 men) = 16 men
Now less men more days 12: 16:: 9: x
Therefore, x = (\(\frac{144}{12}\)) = 12 days
4. A can do a certain job in 12 days. B is 60% more efficient than A. Then Number of days it takes B to do the same piece of work is?
Answer: Option C
Explanation:Ratio of times taken by A and B = 160 : 100 = 8 : 5
If A takes 8 days B takes 5 days
If A takes 12 days, B takes =(\(\frac{5}{8}\) x 12) = 7 ½ days
5. A, B and C together earn Rs.150 per day while A and C together earn Rs. 94 and B and C together earn Rs. 76. The daily earning of C is?
Answer: Option D
Explanation: B’s daily earning = RS.(150 94) = Rs. 56
A’s daily earning = Rs.(150 76) = Rs.74
C’s daily earning = Rs.[150 – (56+74)] = Rs. 20
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