How long will it take 9 men and 6 women to complete a given task?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

How long will it take 9 men and 6 women to complete a given task?

1) 6 men and 3 women take 12 hours to complete a task twice as big as this task.

2) 6 men and 4 women take 19 hours to complete a task thrice as big as this task.

Transforming the original condition and the question, we have working rate of men:m, working rate of women:w, total amount of work: t. Then, we have que=t/(9m+6w)=t/3(3m+2w)=?
In case of 2), (6m+4w)19=2t gives us 19=t/(3m+2w) and therefore t/3(3m+2w)=t/(3m+2w)(1/3)=19/3. The condition is sufficient, therefore the answer is B.

Using variable approach method 1 and transforming the original condition and question practically solves 30% of DS questions

My approach:
I start with statement 2 always
BD/ACE

given 9men and 6 women complete a task in how many hours?
answers are like 6 men and 4 women.. some something related to x+y equation

our question is (9m+6w)*x hours = T..find x
m and w are rates of work.

implies 3(3m+2w)*x hours = T


Statement2:

6 men and 4 women complete a task T three times over in 19 hours.
(6m+4w)*19 = 3T
means
2(3m+2w)*19 = 3T

let 3m+2w be a set of workers P

2P*19 = 3T

question is what is the value of T/3P = x hours

so we can solve it. Statement 2 is SUFFICIENT.

BD/ACE

Statement 1:

(6m+3w)*12 = 2T
3(3m+1w) 12 = 2T

now 3m+1w cannot be P ...so Q
3Q*12 = 2T

question is what is the value of T/3P = x hours

This statement is Not Sufficient

BD/ACE

Is it fair to assume that all men are equally capable? In other words, man 1 and man 2 does the same amount of work in a given unit of time?

Question stem did not specify this information. Hence I answered E

How long will it take 9 men and 6 women to complete a given task?

1) 6 men and 3 women take 12 hours to complete a task twice as big as this task.

2) 6 men and 4 women take 19 hours to complete a task thrice as big as this task.

PROMPT ANALYSIS

Rate of work per hour for men be m and rate for work for women be w. There are 9 men and 6 women.

Superset
The answer could be a positive real number with the unit of time.

Translation.

We need to find time taken to complete (9m +6w)t amount of work, where t is the time taken. We need.
1#total quantity of work.
2# exact value of m and w.
3# two equations to find m and w.

Statement analysis
St 1: the value of 2 *work = (6m +3 w)12. Therefore work = (6m+3w)6. Also work = (9m+6w)t
There fore (9m+6w)t = (6m+3w)6. 3 variables. Hence INSUFFICIENT.

St 2: 3*work = (6m+4w)19. Work = (6m+4w)19/3 = (9m+6w)t
2*19*(3m+2w)/3 = 3*(3m+2w)t
t =38/3
ANSWER. Option b

Answer: Option B

Check the attachment for explanation

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How long will it take 9 men and 6 women to complete a given task?

Lets assume that total task to be completed be W and perhour work rate of a man and a woman be m and w respectively.

So we need to find the time taken by 9 men and 6 women to complete W

(9*m + 6*w )* Time taken = W ----Eq 1

1) 6 men and 3 women take 12 hours to complete a task twice as big as this task.
From St .1 , we can form equation connecting m,w and W

(6m + 3 w) * 12 = 2W------- Eq2

On dividing Eq2 by Eq1, terms containing m and w will not get cancelled, so we will not be able to find the time taken.

Statement 1 alone is not sufficient.

2) 6 men and 4 women take 19 hours to complete a task thrice as big as this task.

(6m + 4 w) * 19 = 3W
2(3m + 2 w) * 19 = 3W--------Eq3

On dividing Eq 3 by Eq1

\(\frac{ 2(3m + 2 w) * 19 }{ (9m + 6w )* Time taken }\)= \(\frac{3W}{W}\)

\(\frac{ 2(3m + 2 w) * 19 }{ 3(3m + 2w )* Time taken}\) = 3

\(\frac{2*19}{ 3 * Time taken}\) = 3


Time taken = 38/9 hours

Statement 2 alone is sufficient

Option B is the answer.

Thanks,
Clifin J Francis