Time and work

Vandana has 35 days to complete a project. How much of the project can she finish in one day if she works diligently?

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.

Kavi can finish 1/13 of the work in one day. How many days will it take him to complete the entire task?

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.

Aanya can complete a task 3 times faster than Vanya. They decided to work on a project together, but Aanya finished it 40 days before Vanya. How long does it take 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.

If 12 men can finish a project in 20 days, how many days will it take for 15 men to finish the same project?

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 day, Ishika, Sneha, and Aarush decided to have a competition in toy-making! They found that 10 men can create 20 toys in 12 days, working 12 hours a day. If 24 friends join and work 16 hours a day, how many days will it take them to make 32 toys?

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 can complete a task in 10 days, while Akhil takes 12 days. If they work together, how long will it take them to finish the work?

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.

Three friends, Kiara, Avni, and Neha, can complete a project in 4, 8, and 12 days respectively. If they work together, how many days will it 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.

Aanya and Dhruv teamed up to complete a project in 12 days. Aanya can finish the project alone in 18 days. How many days would it take for Dhruv to finish the project on his own?

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.

Kavya, Tara, and Divya are friends who took on a challenge. Kavya and Tara can complete a task in 3 days, Tara and Divya in 9 days, and Divya and Kavya in 12 days. How long will it take for all three to finish the work together?

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.

Arnav and Aarav are competing to see who can reap a field faster. They find that 6 men or 8 women can finish the job in 86 days. How long would it take if they teamed up with 14 men and 10 women?

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.