Time and work

Imagine Vandana is on a mission to complete a big project in just 35 days! If she works diligently every day, how much of that project will she accomplish in just one day? Let's find out!

Answer explanation

Vandana completes the work in 35 days, so in 1 day, she will complete 1/35 of the work. Therefore, the work she does in 1 day is 1/35 of the total work.

Imagine Kavi is on a mission to complete a magical task! He can finish 1/13 of the work in just one day. If he keeps up this pace, how many days will it take for him to conquer the entire challenge? Let's find out!

Answer explanation

Kavi completes 1/13 of the work in 1 day. To find the total days to complete the work, we take the reciprocal of 1/13, which is 13. Therefore, Kavi will complete the whole work in 13 days.

Once upon a time in a bustling town, there were two friends, Aanya and Vanya, who were known for their incredible work ethic. Aanya could complete a task 3 times faster than Vanya! One day, they decided to take on a big project together. However, Aanya finished the work in 40 days less than Vanya. Can you figure out how long it takes for Aanya and Vanya to complete the work individually? Let’s solve this fun puzzle!

Answer explanation

Let Q's time be x days. Then P's time is x - 40 days. Since P is 3 times faster, P's rate is 3 times Q's. Setting up the equation: 1/(x-40) = 3/x leads to x = 60. Thus, Q takes 60 days and P takes 20 days.

Arjun, Avyaan, and Ishaan are on a mission to complete a big project! If 12 hardworking men can finish the task in 20 days, how many days do you think it will take for 15 enthusiastic men to finish the same project? Put on your thinking caps and let’s find out!

Answer explanation

If 12 men can complete the work in 20 days, the total work is 12 * 20 = 240 man-days. With 15 men, the days required = 240 / 15 = 16 days. Thus, 15 men can complete the work in 16 days.

One sunny day, Ishika, Sneha, and Aarush decided to have a friendly competition in toy-making! They found out that 10 men can create 20 toys in just 12 days, working 12 hours a day. Now, if 24 enthusiastic friends join the fun and work 16 hours a day, how many days will it take them to make 32 toys? Let’s find out!

Answer explanation

10 men make 20 toys in 12 days (1440 hours total). Thus, 1 man makes 1 toy in 72 hours. For 32 toys, 32 men need 2304 hours. With 24 men working 16 hours a day, it takes 6 days to make 32 toys.

Divya and Akhil are on a mission to complete a challenging piece of work. Divya can finish it all by herself in just 10 days, while Akhil takes a bit longer, needing 12 days to get the job done solo. Now, if these two talented friends join forces and work together, how long do you think it will take them to finish the work? Let’s find out!

Answer explanation

A's work rate is 1/10 and B's is 1/12. Together, their combined rate is 1/10 + 1/12 = 11/60. Thus, they will complete the work in 60/11 days, which is approximately 5.45 days.

Once upon a time in a bustling town, three friends decided to tackle a big project together! Kiara could finish the work in just 4 days, while Avni took a bit longer at 8 days, and Neha, the slowest of the trio, needed 12 days to complete the same task. Now, if these three friends join forces and work together, how many days do you think it will take them to finish the project?

Answer explanation

A's work rate is 1/4, B's is 1/8, and C's is 1/12. Together, their combined rate is 1/4 + 1/8 + 1/12 = 13/24. Thus, they complete the work in 24/13 days, which is approximately 1.85 days.

Once upon a time in a bustling town, Aanya and Dhruv decided to team up for a fun challenge: they wanted to complete a big project together! They discovered that by working hand in hand, they could finish the task in just 12 days. However, Aanya was quite the superstar and could complete the same project all by herself in 18 days. Now, the big question is: how many days would it take for Dhruv to finish the project on his own? Let's find out!

Answer explanation

A and B's combined work rate is 1/12. A's rate is 1/18. Thus, B's rate is 1/12 - 1/18 = 1/36. Therefore, B can complete the work alone in 36 days.

Once upon a time, in a bustling town, three friends - Kavya, Tara, and Divya - decided to take on a challenge. Kavya and Tara teamed up and found that they could complete a piece of work in just 3 days! Meanwhile, Tara and Divya discovered that they could finish the same task in 9 days. Not to be outdone, Divya and Kavya figured out that they could wrap it up in 12 days. Now, the big question is: if all three friends, Kavya, Tara, and Divya, join forces, how long will it take them to finish the work together? Can you solve this fun puzzle?

Answer explanation

Let A+B=1/3, B+C=1/9, C+A=1/12. Adding these gives 2(A+B+C)=1/3+1/9+1/12. Solving for A+B+C yields 1/2, so A, B, and C together can finish the work in 2 days.

Imagine Arnav and Aarav are in a friendly competition to see who can reap a field faster! They discover that if 6 men or 8 women can finish the job in 86 days, they wonder how long it would take if they teamed up with 14 men and 10 women. Can you help them figure it out?

Answer explanation

6 men can do the work in 86 days, which means 1 man can do it in 516 days. Thus, 14 men and 10 women (equivalent to 7 men) can do the work together in 51.6 days. Therefore, they will take approximately 51.6 days.