A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ?

Answer: Option B

Explanation:

Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]

10 women 1 day work = 10/400 = 1/40

10 women will finish the work in 40 days

Answer: Option A

Explanation:

To calculate the answer we need to get 1 man per day work and 1 woman per day work.

Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=> 6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90

(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3

9 men and 15 women will finish the work in 3 days

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.

Answer: Option C

Explanation:

Suppose B takes x dáys to do the work.
As per question A will take
\begin{aligned}
2* \frac{3}{4} * x = \frac{3x}{2}days
\end{aligned}

(A+B)s 1 days work= 1/18
1/x + 2/3x = 1/18 or x = 30 days

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