In a club the ratio of men and women is 16:7. The ratio of married men

Question

In a club the ratio of men and women is 16:7. The ratio of married men and married women is 4:3. Find the percentage of married men if 60% of the women are married.

(A) 35%
(B) 42%
(C) 45%
(D) 52.5%
(E) None of these

KarishmaB · Accepted Answer

Ratio of men : women in club is 16:7. So if number of men were 80, number of women in the club would be 35 (multiple of 16:7 for easier calculations).

We know that 60% of women i.e. 3/5th of women are married. So (3/5)th of 35 = 21 women are married.

Ratio of married men:married women = 4:3. If married women are 21, the multiplier is 7 so number of married men would be 4*7 = 28.

% of men who are married = 28/80 * 100 = 35

Answer (A)

gmatophobia · Answer

Lets assume that the number of men as - m
Lets assume that the number of women as - w

Lets assume that the number of married men as - x
Lets assume that the number of married women as - y

Given

\frac{m}{w}  =  \frac{16}{7}  ------ (1)

\frac{x}{y}  =  \frac{4}{3}  ------ (2)

\frac{y}{w}   =  \frac{60 }{ 100 }  ------ (3)

We are asked to find  \frac{x}{m}

Lets substitute equation 2 in equation 3 -

\frac{3x}{4w}   =  \frac{60 }{100}

We have established the relationship between x and w, however we need the relationship between x and m

From equation 1, we know that   w = \frac{7m}{16}

Replacing the value of w in terms of m we get,

\frac{3x}{4w}   =  \frac{60 }{100}

\frac{(16 * 3 * x)}{ (4 * 7 * m)}   =  \frac{60 }{100}

\frac{12 * x }{ 7* m}   =  \frac{60 }{100}

Divide by 12 on both sides -

\frac{ x }{ 7* m}   =  \frac{5 }{100}

Multiply by 7 on both sides we get -

\frac{ x }{ m}   =  \frac{5 * 7 }{100}

\frac{ x }{ m}   =  \frac{35 }{100}

IMO - A

bv8562 · Answer

Let,
The total no. of Men = M
The total no. of Women = W
The total no. of Married Men = P
The total no. of Married Women = Q

\frac{M}{W} = \frac{16x}{7x}
\frac{P}{Q} = \frac{4y}{3y}

Given,
0.6*7x = 3y
4.2x = 3y
 \frac{x}{y} = \frac{5}{7}

∴ M = 16x = 16*5 = 80
and, P = 4y = 4*7 = 28

% of Married Men =  \frac{P}{M}*100 = \frac{28}{80}*100  =  35% (A)

emsgmat · Answer

Hi  Bunuel ,

This is a great and challenging question. Could you provide an OA with a simple solution?

Thanks!

kungfury42 · Answer

This one made me crank up a bit without pen and paper but the question is otherwise manageable.

Let's assume the total number of men as 16x and women as 7x

Let's assume the total number of married men as 4y and married women as 3y

Now we have that 3y is 60% of 7x or essentially (3y)/(7x) = (3)/(5) cancelling 3 from both sides and taking 7 from left to right, we get y/x = 7/5 and this is of great important to us because this ratio will remain constant throughout our case so we will have to retain it and plug it in our next case (men) to arrive at the answer.

% of married men = (4y)/(16x) = (1/4)*(y/x) = (1/4)*(7/5) = 7/20

7 out of 20 is as good as saying 35 out of 100 (multiplying both Numerator and Denominator by 5)

Hence our answer is option A, 35%

Posted from my mobile device

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83090 Harsha GMAT-Club-Forum-jahzrlg7.png

In a club the ratio of men and women is 16:7. The ratio of married men

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In a club the ratio of men and women is 16:7. The ratio of married men

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