In a certain egg-processing plant, every egg must be

[swerve]

In a certain egg-processing plant, every egg must be inspected and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

The OA is C

Source: Princeton Review

[Scott@TargetTestPrep]

In a certain egg-processing plant, every egg must be inspected and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

The OA is C

Source: Princeton Review

We can create the ratio of the accepted eggs to the rejected eggs as 96x : 4x. Note that 100x eggs are processed every day. We can create the equation:

99/1 = (96x + 12)/(4x - 12)

99(4x - 12) = 96x + 12

99(x - 3) = 24x + 3

99x - 297 = 24x + 3

75x = 300

x = 4

Therefore, 100(4) = 400 eggs are processed every day.

Answer: C

[deloitte247]

For original ratio, let total no of eggs = x
$$\frac{Total\ accepted}{Total\ rejected}=\frac{96x}{4x}$$
When additional 12 eggs are accepted, total number of eggs remains unchanged but ratio
$$=\frac{99}{1}$$
Therefore,
$$\frac{96x+12}{4x-12}=\frac{99}{1}$$
$$\left(96x+12\right)1=99\left(4x-12\right)$$
$$96x+12=396x-1188$$
$$12+1188=396x-96x$$
$$1200=300x$$
$$\frac{1200}{300}=\frac{300x}{300}$$
$$x=4$
$$96x:4x$$
$$=96x+4x$$
$$=96\left(4\right)+4\left(4\right)=$$
$$=384+16=400$$

$$answer\ is\ Option\ C$$

[deloitte247]

For original ratio, let total no of eggs = x
$$\frac{Total\ accepted}{Total\ rejected}=\frac{96x}{4x}$$
When additional 12 eggs are accepted, total number of eggs remains unchanged but ratio
$$=\frac{99}{1}$$
Therefore,
$$\frac{96x+12}{4x-12}=\frac{99}{1}$$
$$\left(96x+12\right)1=99\left(4x-12\right)$$
$$96x+12=396x-1188$$
$$12+1188=396x-96x$$
$$1200=300x$$
$$\frac{1200}{300}=\frac{300x}{300}$$
$$x=4$
$$from\ original\ ratio\ of\ \ 96x:4x$$
$$Total\ no\ of\ processed\ eggs=96x+4x$$
$$=96\left(4\right)+4\left(4\right)=$$
$$=384+16=400$$
$$answer\ is\ Option\ C$$