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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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10 Jan 2022, 09:15
10 Jan 2022, 09:15
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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
(A) 35%
(B) 42%
(C) 45%
(D) 52.5%
(E) None of these
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3128
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
In a club the ratio of men and women is 16:7. The ratio of married men
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10 Jan 2022, 12:09
10 Jan 2022, 12:09
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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
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
In a club the ratio of men and women is 16:7. The ratio of married men
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Updated on: 29 Mar 2023, 23:40
Updated on: 29 Mar 2023, 23:40
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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)
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)
