Correct option is D
Given:
3p + 3q = 36 and 2 × 3p + 3 × 3q = 99,
Solution:
Let:
3ᵖ = a and 3q = b
Then,
a + b = 36 ...(1)
2a + 3b = 99 ...(2)
Multiplying equation (1) by 2:
2a + 2b = 72 ...(3)
Subtracting equation (3) from equation (2):
b = 99 − 72
b = 27
Therefore,
3q= 27 = 3³
Hence,
q = 3
From equation (1):
a + 27 = 36
a = 9
Therefore,
3ᵖ = 9 = 3²
Hence,
p = 2
Now,
A. p + q = 2 + 3 = 5
Therefore, A → II.
B. q − p = 3 − 2 = 1
Therefore, B → I.
C. p² + q² = 2² + 3²
= 4 + 9
= 13
Therefore, C → IV.
D. pq = 2 × 3
= 6
Therefore, D → III.
Hence, the correct matching is:
A-II, B-I, C-IV, D-III
Correct Answer: (d)