Anjali can do a certain piece of work in 16 days. Anjali and Ayushi can together do the same work in 10 days, and Anjali, Ayushi and Ankita can do the same work together in 8 days. In how many days can Anjali and Ankita do the same work?
80/7
Anjali can do a certain piece of work in 16 days, so her work rate is 1⁄16 of the work per day. Anjali and Ayushi can together do the work in 10 days, their combined work rate is 1⁄10. Anjali, Ayushi, and Ankita together can do the same work in 8 days, so their combined work rate is 1⁄8.
Let Anjali's work rate be A, Ayushi's work rate be Y, and Ankita's work rate be K. From the given:
1. A = 1⁄16
2. A + Y = 1⁄10
3. A + Y + K = 1⁄8
We need to find the work rate of Anjali and Ankita together, i.e., A + K.
From equation 1, A = 1⁄16.
Substitute A in equation 2: 1⁄16 + Y = 1⁄10
Y = 1⁄10 - 1⁄16 = 16-10⁄160 = 3⁄80
Substitute A and Y in equation 3:
1⁄16 + 3⁄80 + K = 1⁄8
K = 1⁄8 - (1⁄16 + 3⁄80)
Calculate 1⁄16 + 3⁄80 = 5⁄80 + 3⁄80 = 8⁄80 = 1⁄10
K = 1⁄8 - 1⁄10 = 10-8⁄80 = 1⁄40
So, Anjali and Ankita together: A + K = 1⁄16 + 1⁄40 = 40⁄640 + 16⁄640 = 56⁄640 = 7⁄80
Thus, the days Anjali and Ankita take to complete work: 1⁄(7⁄80) = 80⁄7
Therefore, Anjali and Ankita can do the work together in 80/7 days.
Important Questions from Work and Wages
A and B can complete a piece of work in 120 days. B and C can complete it in 150 days, and A and C can complete it in 200 days. In hoe many days can B alone complete two-fifths of the same work ?
A book has 250 pages. Person A reads 6 pages in an hour. Person B reads 8 pages in an hour. There are two chapters of 72 pages that are difficult for person B to read in the book, so person B takes double the time to read those pages. Who among them will finish the book first and how much sooner than the other?
Efficiencies of P, Q, R and S in doing a job are in the ratio 2 : 3 : 5 : 4. The wages paid for the job are Rs.4200. Who is paid the largest amount and how much is paid?
P and Q can complete a job in 6 and 8 days individually. They both finish the job with the help of R in 3 days. How much wages are to be paid to R. if the total wages are Rs. 3200?
Pravin can do a piece of work in 6 hours. Rishi can do it in 28 hours. With the assistance of Shan, they completed the work in 4 hours. In how many hours can Shan alone do it?
