This is a similar case of 2 variables and 2 equations.

Let the number of workers and supervisors be W and S.

Equation 1:
W/S = 30/1
=> W = 30S

Equation 2:
(W + 50) / (S + 5) = 25/1
=> W + 50 = 25 (S + 5)
=> W + 50 = 25S + 125
=> W = 25S + 75

Equating W from equations 1 and 2,
30S = 25S + 75
=> 5S = 75
=> S = 15

Hence the answer is (A)

Let the common multiplier for ratio be x

workers = 30x
Sup = x

After addition
workers = 30x + 50
Sup = x + 5

New ratio = 25:1

(30x+50):(x+5) = 25:1
solve for x
x = 15 = Initial Supervisors

ans A

Given: \(\frac{workers}{supervisors}=\frac{30x}{x}\), for some positive multiple \(x\).

Also: \(\frac{30x+50}{x+5}=25\) --> \(x=15\) --> \(supervisors=x=15\).

Answer: A.
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Hi Bunnel, I was able to do it with algebra. Is there any other way of estimating the answer as this looks fairly simple question so I am sure there has to be some technique to estimate the answer without doing the whole algebra!

Thanks in Advance!

It should be A.
w/s =30/1 => w=30s

(w+50)/(s+5)=25/1 =>
w+50 =25s+125
(30s) + 50 = 25s + 125
5s = 75
s = 15

You could simply plug in answer choice C (because 10 is a very easy number to multiply) and see if it works. In this case, if there were intially 10 Supervisors, there would have been 300 workers. Adding 50 workers, yields 350 and adding 5 Supervisors gives 15 total. 350:15 does not provide a 25:1 ratio - it is less. Thus, we would need more workers per Supervisor to make this work.

If there were initially 12 Supervisor's, you'd have 360 workers. Adding the new W's and S's gives us 410:17 ==> still less than 25:1

Using 15 Supervisors to start, would mean 450 workers. Adding the new W's and S's, gives us 500:20 and viola, we have our 25:1 ratio.

Many will argue that this is not simpler than working the algebra. But, conceptually, it might be easier to understand. Hope it helps.
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w:s = 30:1

30x + 50 / x + 5 = 25 / 1
x = 15

Answer is A.
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