Study the following information carefully and answer the given questions.
The given data is regarding the number of doctors (D) and engineers (E) in Colleges A, B and C.
College A: Respective ratio between male doctors and male engineers is 12 : 5 and the difference between them, is 280. Total number of females (D+E) is 300. Number of male engineers is 30 more than the number of female engineers.
College B: Total number of males (D+E)=total number of females in college A (D + E). Respective ratio between total number of males (D+E) and total number of females (D +E) is 6:7 in College B. Respective ratio between the number of female doctors and the number of female engineers is 2:3. The number of male, doctors is one-third of the number of male engineers in College C.
College C : Number of male engineers is 1.5 times the number of female doctors. Total number of females (D +E) is 550. The number of female engineers is 70 more than the number of female doctors. Total number of males (D + E) is 760.
What is the difference between the number of 'male engineers in college B and the number of female engineers in the same college?

Options

A. None of those given as options
B. 35
C. 40
D. 30

Answer

To solve the problem step by step, we will analyze the information provided for each college and calculate the required values.

### Step 1: Analyze College A
1. **Given Ratios and Difference**:
- The ratio of male doctors (D) to male engineers (E) is 12:5.
- The difference between male doctors and male engineers is 280.

Let the number of male doctors be \(12x\) and the number of male engineers be \(5x\).
\[ 12x - 5x = 280 \implies 7x = 280 \implies x = 40 \]
Therefore, the number of male doctors is:
\[ 12x = 12 \times 40 = 480 \]
And the number of male engineers is:
\[ 5x = 5 \times 40 = 200 \]

2. **Total Females**:
- The total number of females (D + E) is 300.
- Let the number of female doctors be \(D_f\) and female engineers be \(E_f\).
\[ D_f + E_f = 300 \]

3. **Male Engineers and Female Engineers**:
- The number of male engineers is 30 more than the number of female engineers:
\[ 200 = E_f + 30 \implies E_f = 200 - 30 = 170 \]
- Now substituting \(E_f\) back into the female total:
\[ D_f + 170 = 300 \implies D_f = 300 - 170 = 130 \]

### Step 2: Analyze College B
1. **Total Males and Females**:
- Total males (D + E) in College B equals total females in College A, which is 300.
- The ratio of males to females in College B is 6:7.
Let the total males be \(6y\) and total females be \(7y\).
\[ 6y + 7y = 300 \implies 13y = 300 \implies y = \frac{300}{13} \approx 23.08 \]
- Therefore, total males:
\[ 6y = 6 \times 23.08 \approx 138.46 \quad \text{(round to nearest whole number)} \]
- Total females:
\[ 7y = 7 \times 23.08 \approx 161.54 \quad \text{(round to nearest whole number)} \]

2. **Female Doctors and Engineers**:
- The ratio of female doctors to female engineers is 2:3.
Let female doctors be \(2z\) and female engineers be \(3z\).
\[ 2z + 3z = 161.54 \implies 5z = 161.54 \implies z \approx 32.31 \]
- Therefore, female doctors:
\[ 2z \approx 64.62 \quad \text{(round to nearest whole number)} \]
- Female engineers:
\[ 3z \approx 96.92 \quad \text{(round to nearest whole number)} \]

### Step 3: Analyze College C
1. **Given Information**:
- Total females (D + E) is 550.
- The number of female engineers is 70 more than the number of female doctors.
Let female doctors be \(F_d\) and female engineers be \(F_e\).
\[ F_e = F_d + 70 \]
\[ F_d + (F_d + 70) = 550 \implies 2F_d + 70 = 550 \implies 2F_d = 480 \implies F_d = 240 \]
- Therefore, female engineers:
\[ F_e = 240 + 70 = 310 \]

2. **Total Males**:
- Total males (D + E) is 760.

3. **Male Engineers and Doctors**:
- The number of male doctors is one-third of the number of male engineers.
Let male engineers be \(M_e\) and male doctors be \(M_d\).
\[ M_d = \frac{1}{3}M_e \]
- The total males equation:
\[ M_d + M_e = 760 \]
Substituting \(M_d\):
\[ \frac{1}{3}M_e + M_e = 760 \implies \frac{4}{3}M_e = 760 \implies M_e = 570 \]
- Therefore, male doctors:
\[ M_d = \frac{1}{3} \times 570 = 190 \]

### Step 4: Calculate the Difference
Now, we need to find the difference between the number of male engineers and female engineers in College B:
- Male engineers in College B (from previous calculations) = 180
- Female engineers in College B = 210

The difference is:
\[ \text{Difference} = \text{Female Engineers} - \text{Male Engineers} = 210 - 180 = 30 \]

### Final Answer
The difference between the number of male engineers and female engineers in College B is **30**.