Directions: Given data shows total male and female doctors in three hospital in a seminar. Read data carefully and answer the question:
In annual seminar of three hospitals, A, B and C some male and female doctors represent their hospitals. Average number of female doctors who represent A and B is 210. Total male doctors in A and B is 810. Number of female doctors is `2/3`rd and `2/5`th of male doctor in A and B repectively. Total female doctor who represent C are `25%` more than total female doctor who represent A and total male doctor who represent C are `33 1/3%` more than female doctor who represent B.
`25%` of total female doctor and `20%` of total male doctor who represent B and C together have MBBS degree, then find total who do not have MBBS degree?

Options

A. 812
B. 712
C. 912
D. 622

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Define Variables
Let:
- \( X \) = number of male doctors in Hospital A
- \( Y \) = number of male doctors in Hospital B
- Female doctors in Hospital A = \( \frac{2}{3}X \)
- Female doctors in Hospital B = \( \frac{2}{5}Y \)

### Step 2: Set Up Equations
From the problem, we know:
1. Total male doctors in A and B:
\[ X + Y = 810 \]
2. Average number of female doctors in A and B:
\[ \frac{\frac{2}{3}X + \frac{2}{5}Y}{2} = 210 \]
This simplifies to:
\[ \frac{2}{3}X + \frac{2}{5}Y = 420 \]

### Step 3: Solve the Equations
To solve the second equation, we can eliminate the fractions by multiplying through by 15 (the least common multiple of 3 and 5):
\[ 10X + 6Y = 6300 \]

Now we have a system of equations:
1. \( X + Y = 810 \) (Equation 1)
2. \( 10X + 6Y = 6300 \) (Equation 2)

From Equation 1, we can express \( Y \) in terms of \( X \):
\[ Y = 810 - X \]

Substituting this into Equation 2:
\[ 10X + 6(810 - X) = 6300 \]
\[ 10X + 4860 - 6X = 6300 \]
\[ 4X + 4860 = 6300 \]
\[ 4X = 6300 - 4860 \]
\[ 4X = 1440 \]
\[ X = 360 \]

Now substitute \( X \) back to find \( Y \):
\[ Y = 810 - 360 = 450 \]

### Step 4: Calculate Female Doctors
Now we can calculate the number of female doctors in A and B:
- Female doctors in A:
\[ \frac{2}{3}X = \frac{2}{3} \times 360 = 240 \]
- Female doctors in B:
\[ \frac{2}{5}Y = \frac{2}{5} \times 450 = 180 \]

### Step 5: Calculate Female Doctors in C
Total female doctors in C are 25% more than in A:
\[ \text{Female in C} = 240 + 0.25 \times 240 = 240 + 60 = 300 \]

### Step 6: Calculate Male Doctors in C
Total male doctors in C are 33.33% more than female doctors in B:
\[ \text{Male in C} = 450 + \frac{1}{3} \times 450 = 450 + 150 = 600 \]

### Step 7: Calculate MBBS Degrees
Now we calculate the number of doctors with MBBS degrees:
- Total female doctors in B and C:
\[ \text{Total Female} = 180 + 300 = 480 \]
- 25% of total female doctors have MBBS:
\[ \text{Female with MBBS} = 0.25 \times 480 = 120 \]
- Therefore, female doctors without MBBS:
\[ \text{Female without MBBS} = 480 - 120 = 360 \]

- Total male doctors in B and C:
\[ \text{Total Male} = 450 + 600 = 1050 \]
- 20% of total male doctors have MBBS:
\[ \text{Male with MBBS} = 0.20 \times 1050 = 210 \]
- Therefore, male doctors without MBBS:
\[ \text{Male without MBBS} = 1050 - 210 = 840 \]

### Step 8: Total Doctors without MBBS
Finally, we add the number of doctors without MBBS degrees:
\[ \text{Total without MBBS} = 360 + 840 = 1200 \]

### Final Answer
The total number of doctors who do not have an MBBS degree is **1200**.