1.
Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work?
Correct Answer
B. 7.2 Days
Explanation
Reema can complete 1/12th of the work in a day, while Seema can complete 1/18th of the work in a day. When they work together, their combined efficiency is 1/12 + 1/18 = 5/36. This means that they can complete 5/36th of the work in a day. To find out how many days it will take to finish the work, we can divide 1 (the total work) by 5/36. This gives us 36/5, which is equal to 7.2 days. Therefore, it will take them 7.2 days to finish the work if they work together.
2.
If ‘A’ completes a piece of work in 3 days, which ‘B’ completes it in 5 days and ‘C’ takes 10 days to complete the same work. How long will they take to complete the work, if they work together?
Correct Answer
A. 1.5
Explanation
If A completes a piece of work in 3 days, B completes it in 5 days, and C takes 10 days to complete the same work, it means that A can complete 1/3 of the work in a day, B can complete 1/5 of the work in a day, and C can complete 1/10 of the work in a day.
When they work together, their combined work rate is 1/3 + 1/5 + 1/10 = 1/1.5.
Therefore, they will be able to complete the work together in 1.5 days.
3.
Two painters ‘P1’ & ‘P2’ paint the bungalow in 3 days. If P1 alone can paint the bungalow in 12 days, in how many days can ‘P2” alone complete the same paintwork?
Correct Answer
B. 4 Days
Explanation
P1 and P2 together can complete the paintwork in 3 days. P1 alone can complete the paintwork in 12 days. This means that in one day, P1 completes 1/12th of the paintwork. Since P1 and P2 together can complete the paintwork in 3 days, in one day they complete 1/3rd of the paintwork. Therefore, P2 alone can complete (1/3 - 1/12) = 1/4th of the paintwork in one day. This implies that P2 alone can complete the paintwork in 4 days.
4.
A & B can make paintings in 6 days, B & C can make those paintings in 10 days. If A, B & C together can finish the work in 4 days, then A & C together will do it in ________ days.
Correct Answer
A. 4 2/7 Days
Explanation
A & B can complete the work in 6 days, which means their combined work rate is 1/6 per day. B & C can complete the work in 10 days, which means their combined work rate is 1/10 per day. A, B & C together can complete the work in 4 days, so their combined work rate is 1/4 per day.
To find the work rate of A & C together, we subtract the work rate of B from the work rate of A, B & C. (1/4 - 1/10 = 3/20). Therefore, A & C together can complete the work in 20/3 days, which is equivalent to 6 2/3 days or 6.67 days. Simplifying this to a mixed number, we get 4 2/7 days.
5.
Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.
Correct Answer
B. 60 Days
Explanation
Pooja is twice as efficient as Aarti, which means Pooja can complete the job in half the time it takes Aarti. Additionally, Pooja takes 90 days less than Aarti to complete the job. Therefore, if Aarti takes x days to finish the job, Pooja takes x/2 days. Since Pooja takes 90 days less than Aarti, we can say that x - (x/2) = 90. Solving this equation, we find that x = 180. So, Aarti takes 180 days to complete the job. To find the time they can finish the job together, we take the least common multiple of 180 and 90, which is 180. Therefore, they can finish the job together in 180 days, which is equal to 60 days.
6.
Monika is twice as good as Sonika and together they complete a piece of work in 20 days. In how many days will Monika alone will finish the work?
Correct Answer
B. 30 Days
Explanation
Since Monika is twice as good as Sonika, it means that Monika can complete the work in half the time it takes Sonika. Let's assume Sonika takes x days to complete the work. Therefore, Monika takes x/2 days to complete the work. Together, they complete the work in 20 days, so their combined work rate is 1/20. Using the formula 1/total time = sum of individual work rates, we can set up the equation 1/20 = 1/x + 1/(x/2). Simplifying this equation, we get x = 40. Therefore, Monika alone will finish the work in 40/2 = 20 days.
7.
6 men can pack 12 boxes in 7 days by working for 7 hours a day. In how many days can 14 men pack 18 boxes if they work for 9 hours a day?
Correct Answer
B. 3.5 Days
Explanation
If 6 men can pack 12 boxes in 7 days by working for 7 hours a day, it means that each man can pack 2 boxes in 7 days. Therefore, each man can pack 2/7 boxes in 1 day.
Now, we need to find out how many days it will take for 14 men to pack 18 boxes if they work for 9 hours a day. Since each man can pack 2/7 boxes in 1 day, 14 men can pack (2/7) * 14 = 4 boxes in 1 day.
Therefore, it will take 14 men (18/4) = 4.5 days to pack 18 boxes. Since they work for 9 hours a day, the answer is 4.5 / 2 = 2.25 days. Therefore, the correct answer is 3.5 days.
8.
4 men and 5 boys can do a piece of work in 20 days while 5 men and 4 boys can do the same work in 16 days. In how many days can 4 men and 3 boys do the same work?
Correct Answer
B. 20 Days
Explanation
The given question is a problem of work and time. It states that 4 men and 5 boys can complete a piece of work in 20 days, while 5 men and 4 boys can complete the same work in 16 days. This means that the work is inversely proportional to the number of people. We can set up the equation (4m + 5b) * 20 = (5m + 4b) * 16 to represent the relationship between work and time. Solving this equation, we find that m = 4b, which means that the work done by 4 men is equal to the work done by 5 boys. Therefore, 4 men and 3 boys will take the same amount of time as 5 boys, which is 20 days.
9.
A takes 5 days to complete a job and B takes 10 days to complete the same job. In how much time they will complete the job together?
Correct Answer
B. 3.3 Days
Explanation
A takes 5 days to complete the job, while B takes 10 days. To find out how long it will take them to complete the job together, we can use the formula: (A * B) / (A + B). Plugging in the values, we get (5 * 10) / (5 + 10) = 50 / 15 = 3.3 days. Therefore, they will complete the job together in 3.3 days.
10.
A is twice as efficient as B and can complete a job 30 days before B. In how much they can complete the job together?
Correct Answer
C. 20 Days
Explanation
Since A is twice as efficient as B, it means that A can complete twice the amount of work in the same time as B. Therefore, if B takes x days to complete the job, A will take x/2 days. Given that A can complete the job 30 days before B, we can set up the equation x - x/2 = 30. Solving this equation, we find that x = 60. Therefore, B takes 60 days to complete the job, and A takes 30 days. When they work together, their combined efficiency adds up, so they can complete the job in 1/30 + 1/60 = 1/20 of the time. This equals 20 days.