Directions: Read the following information carefully and answer the question based on it.

The table provided below depicts data regarding the inventory of two categories of garments—Cotton and Silk—across five different fulfillment centers (P, Q, R, S, and T). It displays the numerical difference between the number of Cotton garments and Silk garments, along with the percentage share of Cotton garments in relation to the overall inventory of garments for each fulfillment center.

Fulfillment Center	Difference between Cotton and Silk garments	Percentage of Cotton garments relative to total inventory
P	60	62.5%
Q	198	66.5%
R	188	70%
S	76	60%
T	330	72%

The total inventory of garments at Fulfillment Center U is 25% greater than the number of Cotton garments at Fulfillment Center T. If the ratio of Cotton garments at Fulfillment Center P to Silk garments at Fulfillment Center U is 2 : 1, calculate the number of Cotton garments at Fulfillment Center U.

The correct answer is 600.

Step 1: Calculate the total inventory and number of Cotton garments at Fulfillment Center P.
Let the total inventory of garments at Fulfillment Center P be ${\mathrm{Total}}_P$.
Percentage of Cotton garments at Fulfillment Center P = 62.5% = $\frac{5}{8}$
Percentage of Silk garments at Fulfillment Center P = 100% - 62.5% = 37.5% = $\frac{3}{8}$
Difference in percentage = 62.5% - 37.5% = 25% = $\frac{1}{4}$
Given difference between Cotton and Silk garments at Center P = 60

$\frac{1}{4}\times {\mathrm{Total}}_P=60$

${\mathrm{Total}}_P=60\times 4=240$

Number of Cotton garments at Fulfillment Center P ($C_P$):

$C_P=\frac{5}{8}\times 240=150$

Step 2: Calculate the total inventory and number of Cotton garments at Fulfillment Center T.
Let the total inventory of garments at Fulfillment Center T be ${\mathrm{Total}}_T$.
Percentage of Cotton garments at Fulfillment Center T = 72%
Percentage of Silk garments at Fulfillment Center T = 100% - 72% = 28%
Difference in percentage = 72% - 28% = 44%
Given difference between Cotton and Silk garments at Center T = 330

$44\%\times {\mathrm{Total}}_T=330$

${\mathrm{Total}}_T=\frac{330}{0.44}=750$

Number of Cotton garments at Fulfillment Center T ($C_T$):

$C_T=72\%\times 750=0.72\times 750=540$

Step 3: Calculate total inventory and Silk garments at Fulfillment Center U.
Total inventory of garments at Fulfillment Center U (${\mathrm{Total}}_U$) is 25% greater than $C_T$:

${\mathrm{Total}}_U=540+(25\%\times 540)=540+135=675$

Given ratio of Cotton garments at Center P to Silk garments at Center U ($S_U$) is 2 : 1:

$\frac{C_P}{S_U}=\frac{2}{1}$

$\frac{150}{S_U}=2\Rightarrow S_U=\frac{150}{2}=75$

Step 4: Calculate the number of Cotton garments at Fulfillment Center U.
Number of Cotton garments at Fulfillment Center U ($C_U$):

$C_U={\mathrm{Total}}_U-S_U=675-75=600$

Thus, the number of Cotton garments at Fulfillment Center U is 600.