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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.
Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?
- a)3
- b)5
- c)6
- d)8
- e)10
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Direction: To complete a certain work, C working alone takes twice as...
Given that, 3 times A’s daily work = (B + C)’s one day’s work.
⇒ (A + B + C)’s daily work = 4 times A’s daily work.
But (A + B+ C)’s daily work = 1/5
⇒ A’s daily work = 1/20, A takes 20 days to do the work.
Also, given 2 times C’s daily work = (A + B)’s daily work
⇒ 3 times C’s daily work = (A + B + C)’s daily work
But (A + B + C)’s daily work = 1/5
⇒ C’s daily work = 1/15, So C takes 15 days to do the work
⇒ B’s daily work = 1/5 – (1/20 + 1/15) = 1/12
⇒ A, B and C working alone can complete the work in 20 days, 12 days and 15 days
Now a's efficiency is doubled .So now he takes 10 days.
A’s work for 5 days = 5 × 1/10 = ½ work
The remaining half of the work was done by A and C together.
Work done by A and C in a day = 1/10 + 1/15 = ⅙
The number of days they work together = ( ½)/(1/6) = 3 days
Hence, B left after 3 days from the day the work started.
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Direction: To complete a certain work, C working alone takes twice as...
To solve this problem, let's first assign variables to the rates at which A, B, and C can complete the work.
Let:
- The rate at which A can complete the work be "a" (in units of work per day),
- The rate at which B can complete the work be "b" (in units of work per day), and
- The rate at which C can complete the work be "c" (in units of work per day).
Given information:
1. C working alone takes twice as long as A and B working together.
- This means that the ratio of their rates is 1:2, or a:b = 1:2.
- Therefore, C's rate can be expressed as c = 2a + 2b.
2. A working alone takes 3 times as long as B and C working together.
- This means that the ratio of their rates is 3:1, or a:c = 3:1.
- From the previous equation (c = 2a + 2b), we can substitute c with (2a + 2b) in the ratio, giving a:(2a + 2b) = 3:1.
- Simplifying this ratio gives a:b = 3:4.
3. All three together can complete the work in 5 days.
- This means that their combined rate is 1/5 of the work per day, or a + b + c = 1/5.
Now, let's solve the system of equations to find the values of a, b, and c.
Equation 1: a:b = 3:4
- We can choose any convenient values for a and b that satisfy this ratio.
- Let's assume a = 3 and b = 4.
- Therefore, a:b = 3:4.
Equation 2: c = 2a + 2b
- Substituting the assumed values of a and b, we get c = 2(3) + 2(4) = 6 + 8 = 14.
Equation 3: a + b + c = 1/5
- Substituting the values of a, b, and c, we get 3 + 4 + 14 = 1/5.
- Simplifying this equation gives 21 + 14 = 1/5.
- Therefore, 35 = 1/5, or 35/5 = 1.
- Hence, the equation is satisfied.
Now, let's consider the second scenario where A's efficiency becomes twice what it was earlier.
New values:
- Let A's new rate be "a'".
- Since A's new efficiency is twice what it was earlier, a' = 2a.
A and C started the work together, but C left after some time, and A finished the remaining work in 5 days.
Let's assume that C left after "x" days from the start.
Key points:
- In "x" days, A and C working together can complete (a' + c)x units of work.
- In the remaining 5 - x days, A working alone can complete a'(5 - x) units of work.
- The total work completed is equal to 1 (the entire work
Let:
- The rate at which A can complete the work be "a" (in units of work per day),
- The rate at which B can complete the work be "b" (in units of work per day), and
- The rate at which C can complete the work be "c" (in units of work per day).
Given information:
1. C working alone takes twice as long as A and B working together.
- This means that the ratio of their rates is 1:2, or a:b = 1:2.
- Therefore, C's rate can be expressed as c = 2a + 2b.
2. A working alone takes 3 times as long as B and C working together.
- This means that the ratio of their rates is 3:1, or a:c = 3:1.
- From the previous equation (c = 2a + 2b), we can substitute c with (2a + 2b) in the ratio, giving a:(2a + 2b) = 3:1.
- Simplifying this ratio gives a:b = 3:4.
3. All three together can complete the work in 5 days.
- This means that their combined rate is 1/5 of the work per day, or a + b + c = 1/5.
Now, let's solve the system of equations to find the values of a, b, and c.
Equation 1: a:b = 3:4
- We can choose any convenient values for a and b that satisfy this ratio.
- Let's assume a = 3 and b = 4.
- Therefore, a:b = 3:4.
Equation 2: c = 2a + 2b
- Substituting the assumed values of a and b, we get c = 2(3) + 2(4) = 6 + 8 = 14.
Equation 3: a + b + c = 1/5
- Substituting the values of a, b, and c, we get 3 + 4 + 14 = 1/5.
- Simplifying this equation gives 21 + 14 = 1/5.
- Therefore, 35 = 1/5, or 35/5 = 1.
- Hence, the equation is satisfied.
Now, let's consider the second scenario where A's efficiency becomes twice what it was earlier.
New values:
- Let A's new rate be "a'".
- Since A's new efficiency is twice what it was earlier, a' = 2a.
A and C started the work together, but C left after some time, and A finished the remaining work in 5 days.
Let's assume that C left after "x" days from the start.
Key points:
- In "x" days, A and C working together can complete (a' + c)x units of work.
- In the remaining 5 - x days, A working alone can complete a'(5 - x) units of work.
- The total work completed is equal to 1 (the entire work
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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer?
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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer?.
Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer?.
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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. Efficiency of A become twice of the efficiency, A had earlier. Now A and C started the work together but C left after sometime and A finished the remaining work in 5 days. Find out, after how many days from the start did C leave?a)3b)5c)6d)8e)10Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Banking Exams tests.
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