A and B together can do a work in 30 days and A alone can do it in 40 days. In how many days B alone can do this?

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RRB NTPC Exam 19 Jan 2021 click here to view all questions

A and B together can do a work in 30 days and A alone can do it in 40 days. In how many days B alone can do this?

A120 days

B110 days

C80 days

D100 days

Akhilesh ? Apr 18 '25 at 12:52

Correct Answer: [120 days]
Explanation:
Let's determine how long B alone can complete the work.
Steps:
1. Let the total work be 1 unit.
2. A's work rate = \( \frac{1}{40} \) work/day (since A can complete the work in 40 days).
3. Combined work rate of A and B = \( \frac{1}{30} \) work/day (since together they can complete the work in 30 days).
4. B's work rate = Combined rate
- A's rate:
\(\frac{1}{30} - \frac{1}{40} = \frac{4}{120} - \frac{3}{120} = \frac{1}{120}\)

5. Therefore, B alone can complete the work in \( 120 \) days.

Final Answer: \(\boxed{120}\)

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Shailendra, Amit and Suraj can complete a work in 6, 12 and 15 days respectively. Find the time taken to complete the work if they are working together.

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RRB NTPC Exam 19 Jan 2021 click here to view all questions

Shailendra, Amit and Suraj can complete a work in 6, 12 and 15 days respectively. Find the time taken to complete the work if they are working together.

A60/17 days

B60/23 days

C60/19 days

D60/29 days

Akhilesh ? Apr 18 '25 at 12:55

\( \text{Shailendra's rate} = \frac{1}{6} \) per day

\( \text{Amit's rate} = \frac{1}{12} \) per day

\( \text{Suraj's rate} = \frac{1}{15} \) per day

\( \text{Combined rate} = \frac{1}{6} + \frac{1}{12} + \frac{1}{15} \)

\( \begin{aligned} \frac{1}{6} &= \frac{10}{60} \\ \frac{1}{12} &= \frac{5}{60} \\ \frac{1}{15} &= \frac{4}{60} \end{aligned} \)

\( \frac{10}{60} + \frac{5}{60} + \frac{4}{60} = \frac{19}{60} \)

\( \text{Total time taken} = \frac{1}{\frac{19}{60}} = \frac{60}{19} \) days

Final Answer: \(\boxed{\dfrac{60}{19}}\)

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If A, B, and C can do a piece of work in 15, 30, and 60 days respectively. In how many days together they will do the same work?

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RRB NTPC Exam 20 Jan 2021 click here to view all questions

If A, B, and C can do a piece of work in 15, 30, and 60 days respectively. In how many days together they will do the same work?

A10 days

B12 days

C60/11 days

D60/7 days

Akhilesh ? Apr 7 '25 at 21:47

correct answer is: option d) [60/7 days]
Explanation: Let A, B, and C complete the work in 15, 30, and 60 days respectively.
Work done by A in 1 day = \(\frac{1}{15}\)
Work done by B in 1 day = \(\frac{1}{30}\)
Work done by C in 1 day = \(\frac{1}{60}\)
Work done by A, B, and C together in 1 day = \(\frac{1}{15} + \frac{1}{30} + \frac{1}{60}\) = \(\frac{4 + 2 + 1}{60}\) = \(\frac{7}{60}\)
Therefore, the number of days required for A, B, and C to complete the work together = \(\frac{60}{7}\) days.

• Option a: 10 days is incorrect because the combined work rate is faster than this.
• Option b: 12 days is incorrect because the combined work rate is faster than this.
• Option c: 60/11 days is incorrect because the sum of the individual work rates is not 11/60.

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If Jaya and Shushma together can complete a given task together in 40 days, if Jaya left the job after working for 15 days, and the remaining job was done by Shushma in 40 days, then in how many days Shushma can complete the whole work alone?

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RRB NTPC Exam 20 Jan 2021 click here to view all questions

If Jaya and Shushma together can complete a given task together in 40 days, if Jaya left the job after working for 15 days, and the remaining job was done by Shushma in 40 days, then in how many days Shushma can complete the whole work alone?

A64 days

B72 days

C80 days

D56 days

Akhilesh ? Apr 9 '25 at 06:52

correct answer is: 64 days
Explanation: Let's denote the total work as 1 unit.

Jaya and Shushma together can complete the work in 40 days,

so their combined work rate is \( \frac{1}{40} \) per day.

Jaya works for the first 15 days, completing \( 15 \times \frac{1}{40} = \frac{15}{40} = \frac{3}{8} \) of the work.

The remaining work is \(1- \frac{3}{8} = \frac{5}{8} \)

Shushma completes this remaining work in 40 days,

so her work rate is \( \frac{5}{8} \div 40 = \frac{5}{320} = \frac{1}{64} \) per day.

Therefore, Shushma can complete the whole work alone in 64 days

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A can complete a work in 12 days and B can complete the same work in 24 days. Find the time taken by both A and B together to complete the work.

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RRB NTPC Exam 27 Jan 2021 click here to view all questions

A can complete a work in 12 days and B can complete the same work in 24 days. Find the time taken by both A and B together to complete the work.

A8 days

B10 days

C6 days

D9 days

Akhilesh ? Mar 31 '25 at 21:54

correct answer is: option a (8 days)
Explanation: Let A's one day work be \(\frac{1}{12}\) and B's one day work be \(\frac{1}{24}\).
Then, (A + B)'s one day work = \(\frac{1}{12} + \frac{1}{24} = \frac{2+1}{24} = \frac{3}{24} = \frac{1}{8}\).
Therefore, A and B together can complete the work in 8 days.

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