Bissoy.com
Doctors Medicines MCQs Q&A

A and B together can complete a task in 20 days. B and C together can complete the same task in 25 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

A and B together can complete a task in 20 days. B and C together can complete the same task in 25 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone? Correct Answer 7 : 13

Let, Efficiency of A = x/day

Efficiency of B = y/day

Efficiency of C = z/day

∴ (A + B)’s 1 day’s work = 1/20

∴ x + y = 1/20 ----- (1)

∴ (B + C)’s 1 day’s work = 1/25

∴ y + z = 1/25 ----- (2)

∴ (C + A)’s 1 day’s work = 1/30

∴ z + x = 1/30 ----- (3)

From (1) + (2) + (3) we get,

⇒ x + y + y + z + x = 1/20 + 1/25 + 1/30

⇒ 2(x + y + z) = 37/300

⇒ x + y + z = 37/600 ----- (4)

From (4) - (1) we get,

⇒ x + y + z - (x + y) = 37/600 - 1/20

⇒ z = 7/600 ----- (5)

From (3) - (5) we get,

⇒ z + x - z = 1/30 - 7/600

⇒ x = 13/600

∴ A’s 1 day’s work = 13/600

∴ A can complete the work in = 600/13 days

∴ C’s 1 day’s work = 7/600

∴ C can complete the work in = 600/7 days

∴ required ratio,

⇒ 600/13 ∶ 600/7

⇒ 7 ∶ 13

Related Questions

A and B together can complete a task in 40 days. B and C together can complete the same task in 50 days. A and C together can complete the same task in 60 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?
A and B together can complete a work in 20 days. B and C together can complete the same work in 30 days. A and C together can complete the same work in 30 days. The number of days taken by A while completing the same task alone is how many % less or more than the number of days taken by C while completing the same task alone?
Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to Biren alone? A. 11: 9 B. 11 : 3 C. 7 : 9 D. 9 : 11
Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to taken by Biren? A. 11 : 9 B. 11 : 3 C. 7 : 9 D. 9 : 11
If Arif works alone he will take 20 more hours to complete a task than if he works with Babu to complete the task. If Babu work alone, he will take 5 more hours to complete the task than if he works with Arif to complete the task. What is the ratio of the time taken by Arif to than taken by Babu if each of them works alone to complete the task?
A takes 24 day in completing a work alone.Time taken by A in completing 1/3rd of thework is equal to the time taken by B incompleting half of the work. How many dayswill be taken in completing the work if both A& B start working together?
Sharan and Mayukh, working together, can complete a task in 18 days. However, Mayukh works alone and leaves after completing one-third of the task. Then, Sharan takes over and completes the remaining work by himself. As a result, the duo could complete the task in 40 days. How many days would Sharan alone have taken to do the job if Mayukh had worked faster than Sharan?
Sharan and Mayukh, working together, can complete a task in 18 days. However, Mayukh works alone and leaves after completing 1/3 of the task. Then, Sharan takes over and completees the remaining work by himself. As a result, the duo could complete the task in 40 days. How many days would Sharan alone have taken to do the job if Mayuk' had worked faster than Sharan ?
Person A, B and C can complete a task together in 81 days. A and B can completed the same task together in 97.2 days. B and C can complete the same task together in 162 days. In how many days can B alone complete the task?
Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. Two person X and Y together can make 25% of total number of bricks in 4.8 days. Another person Z can make 50 bricks in a day. What is the time taken by person X and Z together to make the total number of bricks? I. Dimensions of a brick is (3cm × 4cm × 5cm) while the dimension of a cuboids when all the bricks are put together is (72cm × 80cm × 50cm) and ratio of number of days taken by X and Y alone to make the total number of bricks is 3 : 2. II. The total number of bricks is 4800 and person Y can make 150 bricks in day. III. Total volume of all the bricks together is 1.008m3 and dimension of a bricks is (5cm × 6cm × 7cm) and time taken by Z to make total number of bricks is 200 % more than the total time taken by person Y to make total number of bricks.