1.
A and B can do a piece of work in 18 days ; B and C can do it in 24 days; A and C can do it in 36 days. In how many days can they do it all working together?
Correct Answer
A. 16
Explanation
A and B can complete the work in 18 days, B and C can complete it in 24 days, and A and C can complete it in 36 days. This means that A, B, and C have different individual work rates. To find the combined work rate, we can find the reciprocal of the time taken for each pair to complete the work and add them together. The combined work rate of A, B, and C is 1/18 + 1/24 + 1/36 = 1/8. Therefore, working together, they can complete the work in 8 days.
2.
A can do a piece of work in 80 days. He works at it for 10 days and then B alone
finished the remaining work in 42 days. The two togther could complete the work
in?
Correct Answer
B. 30 days
Explanation
A can complete the work in 80 days, so in 10 days he completes 1/8th of the work. Let's assume the total work is represented by 1. So, A completes 1/8th of the work in 10 days, which means B completes 7/8th of the work in 42 days. Now, we can find B's daily work rate by dividing 7/8 by 42, which is 1/48. Since A and B are working together, their combined daily work rate is 1/80 + 1/48 = 4/240 + 5/240 = 9/240 = 3/80. To complete the remaining 1/8th of the work, it will take them 80/3 days, which is approximately equal to 26.67 days. Rounding it up, the two together can complete the work in 27 days.
3.
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Correct Answer
D. 12 hr
Explanation
From the given information, we can deduce that A's work rate is 1/4 of the total work per hour.
Similarly, B and C's combined work rate is 1/3 of the total work per hour, and A and C's combined work rate is 1/2 of the total work per hour.
To find B's work rate, we subtract A and C's combined work rate from B and C's combined work rate.
Therefore, B's work rate is 1/3 - 1/2 = 1/6 of the total work per hour.
To find how long B alone will take to do the work, we invert B's work rate, which gives us 6 hours.
Hence, B alone will take 6 hours to complete the work.
4.
A tyre has punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
Correct Answer
C. 24/7
Explanation
The first puncture alone takes 9 minutes to make the tire flat, and the second puncture alone takes 6 minutes. This means that the first puncture is leaking air at a rate of 1/9 of the tire's volume per minute, and the second puncture is leaking air at a rate of 1/6 of the tire's volume per minute. When both punctures are leaking at the same time, their rates of air leakage add up, so the total rate at which the tire is losing air is (1/9) + (1/6) = (2/18) + (3/18) = 5/18 of the tire's volume per minute. Therefore, it will take 18/5 minutes for both punctures together to make the tire flat, which simplifies to 24/7.
5.
A and B can do a piece of work in 45 days and 40 days respectively. They
began to go the work together but A leaves after some days and than B completed
the reaminnig work in 23 days. The number o days after which A left the work
was?
Correct Answer
D. 9
Explanation
A and B can complete 1/45th and 1/40th of the work in a day, respectively. Let's assume they worked together for x days before A left. So, in x days, they completed x/45th + x/40th of the work. The remaining work is 1 - (x/45 + x/40). B completed this remaining work in 23 days, so we can set up the equation (1 - (x/45 + x/40)) = 1/23. Solving this equation, we find x = 9. Therefore, A left the work after 9 days.
6.
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Correct Answer
B. 7
Explanation
The given question provides information about the time taken by 10 women and 10 children to complete a work individually. It is mentioned that 10 women can complete the work in 7 days and 10 children can complete it in 14 days. This implies that the work done by 10 women in a day is equal to the work done by 10 children in 2 days.
To find out how many days it will take for 5 women and 10 children to complete the work, we can consider the work done by 1 woman and 1 child in a day. Since 10 women can complete the work in 7 days, 1 woman will take 10 times longer, i.e., 70 days to complete the work alone. Similarly, since 10 children can complete the work in 14 days, 1 child will take 10 times longer, i.e., 140 days to complete the work alone.
Now, when we have 5 women and 10 children working together, the total work done in a day will be 5 times the work done by 1 woman plus 10 times the work done by 1 child. Therefore, the total work done in a day will be (5/70) + (10/140) = 1/14 + 1/14 = 2/14 = 1/7.
This means that 5 women and 10 children working together can complete the work in 7 days. Hence, the correct answer is 7.
7.
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 in 13 days. In how many days C alone will do the work ?
Correct Answer
B. 24
8.
A and B can together finish a work in 30 days. They workd at it for 20 days and
then B left. The remaining work was done by A alone in 20 more days A alone
can finish the work in?
Correct Answer
A. 60 days
Explanation
A and B can finish the work in 30 days together. This means that in one day, they can complete 1/30th of the work. They worked together for 20 days, so they completed 20/30th of the work. After B left, A had to complete the remaining work, which is 10/30th. A alone took 20 more days to finish this remaining work. So, in one day, A can complete 10/30th of the work. To find out how many days A alone would take to finish the entire work, we can set up a proportion: (10/30) / 1 = 1 / x, where x is the number of days A alone would take. Solving this proportion, we get x = 30. Therefore, A alone can finish the work in 30 days.
9.
A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?
Correct Answer
D. 6 days
Explanation
A does 1/10th of the work in a day, while B does 1/15th of the work in a day. Together, they do 1/10 + 1/15 = 1/6th of the work in a day. Therefore, they will complete the work together in 6 days.
10.
45 men can complete a work in 16 days. Six after they started working, 30 more men joined them. How many days will they now take to complete the remaining work ?
Correct Answer
B. 6
Explanation
45 men can complete a work in 16 days, which means that the total work requires 720 man-days (45 men x 16 days). After working for 6 days, they have completed 45 x 6 = 270 man-days of work. Now, with the addition of 30 more men, the total number of men working is 45 + 30 = 75 men. The remaining work is 720 - 270 = 450 man-days. Therefore, it will take them 450 man-days / 75 men = 6 days to complete the remaining work.