Question

In a certain college in Andhra Pradesh there were 800 students. Among them 320 were normal, 200 with anaemia, 160 with B-complex deficiency and 120 with Vitamin A deficiency. Complete the table and identify the correct statements.

• A. Statements (i) and (ii) are correct
• B. Statements (i) and (iii) are correct
• C. Statements (ii) and (iv) are correct
• D. Statements (iii) and (iv) are correct

Hint:

Remember: \[ \text{Percentage} = \text{Proportion}\times100 \] and \[ \text{Proportion} = \frac{\text{Frequency}}{\text{Total}} \] For quick calculations, first find the proportion and then multiply by 100 to get the percentage.

Answer 1

The Correct Option is B

Step 1: Find the value of A.
For Normal students: \[ \text{Percentage} = \frac{320}{800}\times 100 \] \[ =40\% \] Therefore, \[ {A=40} \]

Step 2: Find the value of B.
For Vitamin A Deficiency: \[ \text{Percentage} = \frac{120}{800}\times100 \] \[ =15\% \] Hence, \[ {B=15} \]

Step 3: Find the value of C.
For B-complex Deficiency: \[ \text{Percentage} = \frac{160}{800}\times100 \] \[ =20\% \] Thus, \[ {C=20} \]

Step 4: Determine \(a\) and \(b\).
The table itself gives: \[ \text{B-complex Deficiency}=160 \] Therefore, \[ {a=160} \] Similarly, \[ \text{Anaemia}=200 \] Hence, \[ {b=200} \]

Step 5: Calculate \(a_1\).
\[ a_1 = \frac{160}{800} \] \[ =0.20 \] Therefore, \[ {a_1=0.20} \]

Step 6: Calculate \(b_1\).
\[ b_1 = \frac{200}{800} \] \[ =0.25 \] Thus, \[ {b_1=0.25} \]

Step 7: Verify Statement (i).
Statement (i): \[ A=40,\quad B=15,\quad C=20, \] \[ a=160,\quad b=200 \] All values are correct. Therefore, \[ {\text{Statement (i) is correct}} \]

Step 8: {Verify Statement (ii).}
Statement (ii) claims: \[ a=100 \] But actual value is \[ a=160 \] Hence, \[ {\text{Statement (ii) is incorrect}} \]

Step 9: {Verify Statement (iii).}
Statement (iii): \[ A=40,\quad B=15,\quad C=20 \] \[ a_1=0.20,\quad b_1=0.25 \] All are correct. Therefore, \[ {\text{Statement (iii) is correct}} \]

Step 10: {Verify Statement (iv).}
Statement (iv) claims: \[ B=20,\quad C=15 \] which is opposite to the actual values. Hence, \[ {\text{Statement (iv) is incorrect}} \]

Step 11: {Final conclusion.}
The correct statements are: \[ (i)\ \text{and}\ (iii) \] Therefore, \[ {\text{Option (2)}} \]