Question Detail

A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in

15 days
10 days
9 days
8 days

Answer: Option A

Explanation:

Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 time

If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 days

1. A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk were ?

\begin{aligned} 14\frac{2}{3}kmph \end{aligned}
\begin{aligned} 15\frac{2}{3}kmph \end{aligned}
\begin{aligned} 16\frac{2}{3}kmph \end{aligned}
\begin{aligned} 17\frac{2}{3}kmph \end{aligned}

Answer: Option C

Explanation:

Work done by A in l0 days = (1/25) *10 = 2/5
Remaining work = 1 - (2/5) = 3/5
(A+B)s 1 days work = (1/25) + (1/20) = 9/100

9/100 work is done by them in 1 day.
hence 3/5 work will be done by them in (3/5)*(100/9)
= 20/3days.

Total time taken = (10 + 20/3) = 16*(2/3) days

2. 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}

3. 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.

4. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

6 days
7 days
8 days
9 days

Answer: Option B

Explanation:

1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work =
\begin{aligned}
\left(\frac{5}{70}+\frac{10}{140}\right) \\
= \frac{1}{7}
\end{aligned}

So 5 women and 10 children will finish the work in 7 days.

5. Rahul and Sham together can complete a task in 35 days, but Rahul alone can complete same work in 60 days. Calculate in how many days Sham can complete this work ?

84 days
82 days
76 days
68 days

Answer: Option A

Explanation:

As Rahul and Sham together can finish work in 35 days.
1 days work of Rahul and Sham is 1/35
Rahul can alone complete this work in 60 days,
So, Rahul one day work is 1/60
Clearly, Sham one day work will be = (Rahul and Sham one day work) - (Rahul one day work)
\begin{aligned}
= \frac{1}{35} - \frac{1}{60} \\
= \frac{1}{84} \\
\end{aligned}

Hence Sham will complete the given work in 84 days.