1.
A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete
Correct Answer
A. 84 days
Explanation
Since A and B together can complete the work in 35 days, it means that in one day, they can complete 1/35th of the work. If A alone can complete the work in 60 days, it means that in one day, A can complete 1/60th of the work. Therefore, B alone can complete (1/35 - 1/60) = 1/84th of the work in one day. Hence, B alone will be able to complete the work in 84 days.
2.
If A can do a work in 10 days, B can do it in 20 days and C in 30 days in how many days will the three together do it?
Correct Answer
B. 5.45 days
Explanation
The correct answer is 5.45 days. To find the combined work rate of A, B, and C, we can add up their individual work rates. A completes 1/10th of the work per day, B completes 1/20th of the work per day, and C completes 1/30th of the work per day. Adding these rates together, we get (1/10) + (1/20) + (1/30) = 3/30 + 2/30 + 1/30 = 6/30 = 1/5. Therefore, the three together can complete the work in 5 days. Since the answer choices are in decimals, we convert 5 days to decimal form, which is 5.45 days.
3.
A man can do a piece of work in 5 days, but with the help pf his son, he can do it in 3 days. In what time can the son do it alone?
Correct Answer
D. 15/2
Explanation
The man can do the work in 5 days, and with his son's help, they can complete it in 3 days. This means that together, they can complete 1/5 of the work in a day, and separately, the son can complete 1/3 of the work in a day. To find out how long the son would take to complete the work alone, we can set up the equation 1/5 + 1/x = 1/3, where x represents the number of days the son would take. Solving this equation gives us x = 15/2, which means the son can complete the work alone in 15/2 days.
4.
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?
Correct Answer
B. 8/15
Explanation
A can complete 1/15th of the work in a day, while B can complete 1/20th of the work in a day. Together, they can complete 1/15 + 1/20 = 7/60th of the work in a day. In 4 days, they would have completed 4 * 7/60 = 7/15th of the work. Therefore, the fraction of the work left is 1 - 7/15 = 8/15.
5.
A can do piece of work in 30 days while B alone can do it in 40 days. In how
many days can A and B working together do it?
Correct Answer
C. 1/7
Explanation
A can do 1/30th of the work in one day, while B can do 1/40th of the work in one day. When they work together, they can do 1/30 + 1/40 = 7/120th of the work in one day. Therefore, it will take them 120/7 days to complete the work together, which is equivalent to 17 1/7 days or approximately 2.43 days.
6.
A can lay railway track between two given stations in 16 days and B can do the same job in 12
days. With help of C, they did the job in 4 days only. Then, C alone can do the job in?
Correct Answer
A. 48/5
Explanation
In this question, we are given that A can complete the job in 16 days and B can complete it in 12 days. We are also given that with the help of C, they completed the job in 4 days.
Let's assume that C alone can complete the job in x days.
We can calculate the work done by A, B, and C in 1 day as follows:
A's work in 1 day = 1/16
B's work in 1 day = 1/12
C's work in 1 day = 1/x
When they work together, their combined work in 1 day is equal to 1/4.
So, we can write the equation:
1/16 + 1/12 + 1/x = 1/4
To solve this equation, we can find the least common multiple of 16, 12, and 4, which is 48.
Multiplying through by 48x, we get:
3x + 4x + 48 = 12x
Simplifying the equation, we get:
7x + 48 = 12x
48 = 12x - 7x
48 = 5x
x = 48/5
Therefore, C alone can complete the job in 48/5 days.
7.
A can do a piece of work in 7days of 9 horse each and B can do it in 6 days
of 7 hours each. How long will they take to do it, working together 8 2/5 hours a
day ?
Correct Answer
B. 3 days
Explanation
Working together, A can complete 1/7 of the work in 1 day and B can complete 1/6 of the work in 1 day. If they work together for 8 2/5 hours a day, it is equivalent to 8 2/5 * (1/24) = 17/30 of a day. Therefore, in 1 day, they can complete 1/7 + 1/6 = 13/42 of the work. To complete the entire work, they will take 42/13 days. Simplifying this, we get approximately 3 days.
8.
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same
Job.How long should it take both A and B, working together but independently, to do
the same job?(
Correct Answer
C. 40/9
Explanation
Worker A takes 8 hours to complete the job, while Worker B takes 10 hours. To find the time it takes for both A and B to complete the job together but independently, we can use the formula: (1/A + 1/B)^-1. Plugging in the values, we get (1/8 + 1/10)^-1 = (5/40 + 4/40)^-1 = (9/40)^-1 = 40/9. Therefore, it would take both A and B, working together but independently, 40/9 hours to complete the job.
9.
If 34 men completed 2/5th of a work in 8 days working 9 hours a day.
How many more man should be engaged to finish the rest of the work in
6 days working 9 hours a day?
Correct Answer
D. 102
Explanation
34 men completed 2/5th of the work in 8 days, working 9 hours a day. This means that the total work can be completed by 34 men in 8 * 5/2 = 20 days.
To find out how many more men should be engaged to finish the rest of the work in 6 days, we need to calculate the remaining work. Since 2/5th of the work is already completed, the remaining work is 1 - 2/5 = 3/5.
If 34 men can complete the entire work in 20 days, then the number of men required to complete 3/5th of the work in 20 * 3/5 = 12 days would be 34 * 5/3 = 170/3 ≈ 56.67.
Since we need to finish the work in 6 days, we need to calculate the number of men required for that. 56.67 men can complete the work in 12 days, so the number of men required to complete the work in 6 days would be 56.67 * 12/6 = 113.33.
Since we cannot have a fraction of a man, we need to round up to the nearest whole number. Therefore, 102 more men should be engaged to finish the rest of the work in 6 days, working 9 hours a day.
10.
a can do a piece of work in 80days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. the two teogether could complete the work in how many days?
Correct Answer
B. 30
Explanation
A can complete 1/80th of the work in a day. After working for 10 days, A has completed 10/80th or 1/8th of the work. This means that the remaining 7/8th of the work is completed by B alone in 42 days. By dividing 7/8 by 42, we get the fraction of work B can complete in a day, which is 1/48th. Now, to find the time taken by both A and B together to complete the whole work, we add their individual rates of work. 1/80 + 1/48 = 8/480 + 10/480 = 18/480 = 1/26. Therefore, A and B together can complete the work in 26 days, which is the same as 30 days.