Quantitative Apptitude - Time And Work Online Test 5

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.

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.

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.

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.

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.

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.

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.

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.