The Fishery Diner at the start of business operations had lobsters and

Original ratio: \(\frac{L}{F}= \frac{2x}{5x}\)

No fish added, two lobsters added, and the new ratio is 1 : 2, i.e., \(\frac{1}{2}\)

\(\frac{2x +2}{5x} = \frac{1}{2}\)

\(2(2x +2) = 5x\)
\(4x + 4 = 5x\)
\(x = 4 =\) the multiplier for the original ratio

How many lobsters at the start?
\(x = 4\)
Lobsters (original ratio)
\(= 2x = (2)(4) = 8\)

Answer D

Let the initial number of lobsters and fish be 2x and 5x respectively.

After adding 2 lobsters, the total number of lobster = 2x + 2

The new ratio = 1: 2

2x+2 : 5x = 1: 2

4x + 4 = 5x

x = 4

Thus, the initial number of lobster = 2x = 8.

Correct Answer : Option D

Method 2

Though the usual method is the quickest way to solve, an alternate method could be the following.

Initial ratio- 2: 5

Final ratio - 1: 2 or 5/2: 5 = 2.5: 5

Notice that the number of fishes are not changing, so I tried to keep the 5 intact in both the ratios, so that I can now simply focus on the number of lobster.

2 becomes, 2.5 when 2 lobsters are added, so we can say that 0.5 in the ratio is equivalent to 2 lobster in acutal.

We need to find the initial number of lobster(i.e 2 in the ratio), so using unitary method, we can say

0.5 is equivalent to 2 lobsters
1 is equivalent to 4 lobsters
Thus, 2 is equivalent to 8 lobsters.

Such ratio manipulation can be helpful in a lot of sums, so thought of sharing this method.


Regards,
Saquib
e-GMAT
Quant Expert