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9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work?
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9. A and B can do a piece of work in 18 days; B and C can do it in 24 ...
Given information:
A + B = 1/18
B + C = 1/24
A + C = 1/36
To find: Number of days it takes for B to finish the work alone.
Let's solve the problem step by step.
Step 1: Find the individual efficiencies of A, B, and C.
Let's assume the efficiency of A is x units per day, the efficiency of B is y units per day, and the efficiency of C is z units per day.
From the given information, we can write the following equations:
x + y = 1/18 ...(1)
y + z = 1/24 ...(2)
x + z = 1/36 ...(3)
Step 2: Solve the equations (1), (2), and (3) simultaneously.
To solve the equations, we can use the method of substitution or elimination. Here, we will use the elimination method.
Multiplying equation (1) by 24, equation (2) by 18, and equation (3) by 36, we get:
24x + 24y = 1/18 * 24 ...(4)
18y + 18z = 1/24 * 18 ...(5)
36x + 36z = 1/36 * 36 ...(6)
Simplifying equations (4), (5), and (6), we get:
24x + 24y = 4/3 ...(7)
18y + 18z = 3/4 ...(8)
36x + 36z = 1 ...(9)
Multiplying equation (7) by 3, equation (8) by 4, and equation (9) by 4, we get:
72x + 72y = 4 ...(10)
72y + 72z = 3 ...(11)
144x + 144z = 4 ...(12)
Subtracting equation (11) from equation (10), we get:
72x + 72y - (72y + 72z) = 4 - 3
72x - 72z = 1 ...(13)
Adding equation (12) to equation (13), we get:
144x + 144z + 72x - 72z = 4 + 1
216x = 5
x = 5/216
Substituting the value of x in equation (3), we get:
(5/216) + z = 1/36
z = 1/36 - 5/216
z = 6/216 - 5/216
z = 1/216
Substituting the values of x and z in equation (1), we get:
(5/216) + y = 1/18
y = 1/18 - 5/216
y = 12/216 - 5/216
y = 7/216
Step 3: Find the number of days B alone can finish the work.
We know that B's efficiency is y units per day.
Therefore, B can finish the work alone in (1/y) days.
Substituting the value of y, we get:
(1/(7/216)) = 216/7
Thus, B alone can finish the
A + B = 1/18
B + C = 1/24
A + C = 1/36
To find: Number of days it takes for B to finish the work alone.
Let's solve the problem step by step.
Step 1: Find the individual efficiencies of A, B, and C.
Let's assume the efficiency of A is x units per day, the efficiency of B is y units per day, and the efficiency of C is z units per day.
From the given information, we can write the following equations:
x + y = 1/18 ...(1)
y + z = 1/24 ...(2)
x + z = 1/36 ...(3)
Step 2: Solve the equations (1), (2), and (3) simultaneously.
To solve the equations, we can use the method of substitution or elimination. Here, we will use the elimination method.
Multiplying equation (1) by 24, equation (2) by 18, and equation (3) by 36, we get:
24x + 24y = 1/18 * 24 ...(4)
18y + 18z = 1/24 * 18 ...(5)
36x + 36z = 1/36 * 36 ...(6)
Simplifying equations (4), (5), and (6), we get:
24x + 24y = 4/3 ...(7)
18y + 18z = 3/4 ...(8)
36x + 36z = 1 ...(9)
Multiplying equation (7) by 3, equation (8) by 4, and equation (9) by 4, we get:
72x + 72y = 4 ...(10)
72y + 72z = 3 ...(11)
144x + 144z = 4 ...(12)
Subtracting equation (11) from equation (10), we get:
72x + 72y - (72y + 72z) = 4 - 3
72x - 72z = 1 ...(13)
Adding equation (12) to equation (13), we get:
144x + 144z + 72x - 72z = 4 + 1
216x = 5
x = 5/216
Substituting the value of x in equation (3), we get:
(5/216) + z = 1/36
z = 1/36 - 5/216
z = 6/216 - 5/216
z = 1/216
Substituting the values of x and z in equation (1), we get:
(5/216) + y = 1/18
y = 1/18 - 5/216
y = 12/216 - 5/216
y = 7/216
Step 3: Find the number of days B alone can finish the work.
We know that B's efficiency is y units per day.
Therefore, B can finish the work alone in (1/y) days.
Substituting the value of y, we get:
(1/(7/216)) = 216/7
Thus, B alone can finish the
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9. A and B can do a piece of work in 18 days; B and C can do it in 24 ...
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9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work?.
9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 9. A and B can do a piece of work in 18 days; B and C can do it in 24 days, A and C can do it in 36 days. In how many days B alone can finish the work?.
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