Question Detail

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C

Rs. 300
Rs. 400
Rs. 500
Rs. 600

Answer: Option B

Explanation:

C's 1 day's work =

$\begin{aligned} \frac{1}{3}- \left(\frac{1}{6} +\frac{1}{8} \right) \\ =\left(\frac{1}{3} - \frac{7}{24} \right) \\ = \frac{1}{24} \\ A:B:C = \frac{1}{6}:\frac{1}{8}:\frac{1}{24} \\ = 4:3:1 \\ C's Share = \frac{1}{8}* 3200 \\ = 400 \end{aligned}$
If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small information, it is the C ratio divided by total ratio.

1. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

$\begin{aligned} 3\frac{1}{5} min \end{aligned}$
$\begin{aligned} 3\frac{2}{5} min \end{aligned}$
$\begin{aligned} 3\frac{3}{5} min \end{aligned}$
$\begin{aligned} 3\frac{4}{5} min \end{aligned}$

Answer: Option C

Explanation:

Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:

1 minute work done by both the punctures =

$\begin{aligned} \left(\frac{1}{9}+\frac{1}{6} \right) \\ =\left(\frac{5}{18} \right) \\ \end{aligned}$

So both punctures will make the type flat in

$\begin{aligned} \left(\frac{18}{5} \right)mins \\ = 3\frac{3}{5} mins \end{aligned}$

2. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.

$\begin{aligned} \frac{4}{9} \end{aligned}$
$\begin{aligned} 2\frac{4}{9} \end{aligned}$
$\begin{aligned} 3\frac{4}{9} \end{aligned}$
$\begin{aligned} 4\frac{4}{9} \end{aligned}$

Answer: Option D

Explanation:

In this type of questions, first we need to calculate 1 hours work, then their collective work as,

A's 1 hour work is 1/8
B's 1 hour work is 1/10

(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40

So both will finish the work in 40/9 hours
=

$\begin{aligned} 4\frac{4}{9} \end{aligned}$

3. A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?

$\begin{aligned} 7\frac{1}{2}days \end{aligned}$
$\begin{aligned} 6\frac{1}{2}days \end{aligned}$
$\begin{aligned} 5\frac{1}{2}days \end{aligned}$
$\begin{aligned} 4\frac{1}{2}days \end{aligned}$

Answer: Option A

Explanation:

In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As,

Son's one day work =

$\begin{aligned} \left(\frac{1}{3}-\frac{1}{5} \right) \\ =\left(\frac{5-3}{15} \right) \\ = \frac{2}{15} \end{aligned}$

So son will do whole work in 15/2 days
which is =

$\begin{aligned} 7\frac{1}{2}days \end{aligned}$

4. A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days ?

$\begin{aligned} 6\frac{1}{2}days \end{aligned}$
$\begin{aligned} 7\frac{1}{2}days \end{aligned}$
$\begin{aligned} 8\frac{3}{5}days \end{aligned}$
$\begin{aligned} 9\frac{3}{5}days \end{aligned}$

Answer: Option D

Explanation:

In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work.
We can do it by,
(A+B+C)'s work - (A's work + B's work).

Let's solve it now:

C's 1 day work =

$\begin{aligned} \frac{1}{4}- \left(\frac{1}{16} +\frac{1}{12} \right) \\ =\left(\frac{1}{4} - \frac{7}{48} \right) \\ = \frac{5}{48} \end{aligned}$

So C can alone finish the job in 48/5 days,
Which is =

$\begin{aligned} 9\frac{3}{5}days \end{aligned}$

5. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

$\begin{aligned} 35\frac{1}{2} \end{aligned}$
$\begin{aligned} 36\frac{1}{2} \end{aligned}$
$\begin{aligned} 37\frac{1}{2} \end{aligned}$
$\begin{aligned} 38\frac{1}{2} \end{aligned}$

Answer: Option C

Explanation:

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 (1/2) days

Question Detail

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C

1. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

2. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.

3. A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?

4. A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days ?

5. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

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Question Detail

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C

1. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

2. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.

3. A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?

4. A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days ?

5. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

Thanks ! Your comment will be approved shortly !

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