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p and q are positive numbers satisfying 3p + 2pq = 4 and 5q + pq = 3. Find the value of p.
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1 or − 9 5 -
1 or − 20 2 3 -
1 or − 20 3 -
1 or − 9 2 5
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Correct Option: C
3p + 2pq = 4
→ p (3 + 2q) = 4
| ⇒ p = | .........(i) | |
| 3 + 2q |
Now, putting the value of p in
5q + pq = 3,
we get
| 5q + | (q) = 3 | |
| 3 + 2q |
| ⇒ | = 3 | |
| 3 + 2q |
⇒ 19q + 10q² = 9 + 6q
⇒ 10q² + 13q – 9 = 0
⇒ 10q² + 18q – 5q – 9 = 0
⇒ 2q (5q + 9) – 1 (5q + 9) = 0
⇒ (2q – 1) (5q + 9) = 0
| ⇒ q = | or - | ||
| 2 | 2 |
Putting q = 1/2 in (i),
| ⇒ p = | = 1 | |
| 3 + 2 × (1/2) |
| putting q = - | |
| 5 |
| = p | |||||||||
| 3 + 2 |  | - |  | ||||||
| 5 | |||||||||
| = | ||
| 15 - 18 |
| = - | ||
| 3 |
