In a certain company, the ratio of male to female employees is 7:8...

Here's a quick solution....

PRESENTLY, the ratio of male to female employees is 7:8
So, there could be 7 males and 8 females
or 14 males and 16 females
21 males and 24 females
etc.

Notice that the PRESENT number of males must be a multiple of 7.
Check the answer choices....
A, C and E are NOT multiples of 7, so we can eliminate them.
This leaves us with answer choices B and D.

If 3 more men were hired, this ratio would increase to 8:9
So, if we add 3 to our two remaining answer choices, the result must be a multiple of 8
B) 21 + 3 = 24. 24 IS a multiple of 8. So keep it
D) 189 + 3 = 192. 192 IS a multiple of 8. So keep it

So, we're forced to check ONE of the answer choices. If it works, then that's the correct answer. If it doesn't work, then the OTHER answer is correct.
Let's check answer choice B.

B) If there are 21 males, then there are 24 females (simplifies to a 7:8 ratio).
When we add 3 males, we get 24 males and 24 females. This simplifies to a 1:1 ratio, but we want an 8:9 ratio.
ELIMINATE B

Answer:

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Another approach is to use TWO variables.
Let M = present number of males
Let F = present number of females

The ratio of male to female employees is 7:8
So, M/F = 7/8
Cross multiply to get 7F = 8M


If 3 more men were hired, this ratio would increase to 8:9
So, (M+3)/F = 8/9
Cross multiply to get 9(M+3) = 8F
Expand: 9M + 27 = 8F

We now have a system of two equations and two variables:
7F = 8M
9M + 27 = 8F

Solve to get: M = 189 and F = 216

Answer: still D!

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\(\frac{Male}{Female} = \frac{7}{8}\) after adding 3 more men \(\frac{Male}{Female} = \frac{8}{9}\)

Check the options -

1. The correct answer choice will be divisible by 7 ( Only B & D are possible )
2. The correct answer choice +3 will be divisible by 8 ( Only B & D are possible )

Now , check any one option , lets say (B) -

\(\frac{Male}{Female} = \frac{21}{24}\)

After adding 3 more men \(\frac{Male}{Female} = \frac{24}{24}\) = 1 ( Hence not possible )

Check Option (D) -

\(\frac{Male}{Female} = \frac{189}{216}\)

After adding 3 more men \(\frac{Male}{Female} = \frac{192}{216}\) = 8:9

Hope this helps...

Am bit confused - Why are we multiplying with the original ratio to get the ans i.e 27*7 ? why not with 8 since after increasing by 3 since new ratio would be 8/9?

please help!

3 more men is hypothetical scenario: "If 3 more men were hired, this ratio would increase to 8:9..."

(7x+3)/(8x)=8/9. Solve to get x = 27. That gives the number of men as 189. Hence option D

Just 2 cents :
Question could have been more clearer if it were mentioned , how many male were there originally?
Just of now question is just a little ambiguous as to whether the male employees after the change or before the change is being asked for.

another approach is substitution:
m/f=7/8
f=8m/7
substituting,
(m+3)/(8m/7)=8/9
m=189
D

A ratio of 7:8 means, males are 12.5% as compared to females.
A ratio of 8:9 means, males are 11.11% as compared to females.

Since an increase of 3 in number corresponds to a decrease of significantly less than 3%, the total number of males must be more than 100. Thus, options A,B, and C can be eliminated. We are left with options D and E only. Option E is not divisible by 7, so it can be eliminated (man cannot be in a fraction).

D is Correct