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.
Total number of females (D + E) in college C is approximately what percent less than the total number of males (D + E) in college A?

Options

A. 4
B. 34
C. 28
D. 19

Answer

To solve the problem step-by-step, let's break down the information provided for each college and calculate the required values.

### Step 1: Analyze College A
1. **Given Ratios and Differences**:
- 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:
- Male doctors = \( 12 \times 40 = 480 \)
- Male engineers = \( 5 \times 40 = 200 \)

2. **Total Males in College A**:
\[ \text{Total males} = 480 + 200 = 680 \]

3. **Total Females**:
- Total number of females (D + E) is given as 300.

### Step 2: Analyze College B
1. **Total Males and Females**:
- Total number of males (D + E) in College B = Total number of females in College A = 300.
- The ratio of total males to total females in College B is 6:7.

Let the total males in College B be \( 6y \) and total females be \( 7y \).

Since total males = 300:
\[ 6y = 300 \implies y = 50 \]
Therefore:
- Total males = \( 6 \times 50 = 300 \)
- Total females = \( 7 \times 50 = 350 \)

2. **Female Doctors and Engineers Ratio**:
- The ratio of female doctors to female engineers is 2:3.
Let female doctors = \( 2z \) and female engineers = \( 3z \).

\[ 2z + 3z = 350 \implies 5z = 350 \implies z = 70 \]
Therefore:
- Female doctors = \( 2 \times 70 = 140 \)
- Female engineers = \( 3 \times 70 = 210 \)

### Step 3: Analyze College C
1. **Given Information**:
- Total number of females (D + E) = 550.
- The number of female engineers is 70 more than the number of female doctors.

Let female doctors = \( F_d \) and female engineers = \( F_e \).
\[ F_e = F_d + 70 \]
\[ F_d + F_e = 550 \implies F_d + (F_d + 70) = 550 \implies 2F_d + 70 = 550 \implies 2F_d = 480 \implies F_d = 240 \]
Therefore:
- Female engineers = \( 240 + 70 = 310 \)

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

### Step 4: Calculate Percent Difference
1. **Calculate the difference between total females in College C and total males in College A**:
\[ \text{Difference} = 680 - 550 = 130 \]

2. **Calculate the percentage difference**:
\[ \text{Percentage} = \left( \frac{130}{680} \right) \times 100 \]
\[ = \frac{13000}{680} \approx 19.12\% \]

### Final Answer
The total number of females (D + E) in College C is approximately **19% less** than the total number of males (D + E) in College A.

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