Read the information and answer the following questions.

The table shows the number of males working in private and public companies and number of females working in private and public company in four (A, B, C & D) different cities.

Cities	Males in Private company	Males in Public company	Females (private + public)
A	15x – 2y	y	55
B	16x	16	108
C	9y	24	74
D	84	21	85

Note – (i) Number of male employees in A are 50.

(ii) Total males working in private company from B and C are 154.
(iii) Total employees (male + female) working in any city = private companies + public company
(iv) Males/females working in any city = Sum of males/females working in private and public company

In city A, 40% of the females working in private company, then find the ratio females working in public companies from A to total males working in city D.

The correct option is 11:35.

Let's solve the problem step-by-step using the given table and conditions.

Step 1: Find the values of $x$ and $y$

From Note (ii), the total males working in private companies from city B and city C is 154.

Males in private company from B = $16x$

Males in private company from C = $9y$

So,

$16x+9y=154$    --- (Equation 1)

From Note (i), the total number of male employees in city A is 50.

Total males in A = (Males in Private company in A) + (Males in Public company in A)

$(15x-2y)+y=50$

$15x-y=50$

$y=15x-50$    --- (Equation 2)

Now, substitute Equation 2 into Equation 1:

$16x+9(15x-50)=154$

$16x+135x-450=154$

$151x=154+450$

$151x=604$

$x=4$

Now, substitute $x=4$ into Equation 2 to find $y$:

$y=15\left(4\right)-50=60-50=10$

Step 2: Find the number of females working in public companies in City A

From the table, the total number of females (private + public) in city A = 55.

Given that 40% of the females in city A work in private companies:

Females in private company in A = $40\%\text{ of }55=\frac{40}{100}\times 55=22$

Therefore, females working in public companies in A = Total females in A - Females in private company in A

$\text{Females in public company in A}=55-22=33$

Step 3: Find total males working in City D

From the table for city D:

Males in private company = 84

Males in public company = 21

Total males in city D = $84+21=105$

Step 4: Calculate the required ratio

Ratio = (Females in public company in A) : (Total males in city D)

$\text{Ratio}=33:105$

Dividing both sides by 3:

$\text{Ratio}=11:35$