If 2p 3q 12 and 4p2 4pq minus 3q2 126 then what is the value of p 2q ........

Quantitative Aptitude (CDS) Quadratic Equations

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If 2p + 3q = 12 and 4p² + 4pq − 3q² = 126 , then what is the value of p + 2q ?

21 / 4

25 / 4

99 / 16

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Explanation:

As,
2p+3q=12 ………. (i)
And 4p²+4pq−3q²=126
=> (2p)²+2×2p×q+q²−4q²=126
=> (2p+q)²−(2q)²=126
=> (2p+q+2q)(2p+q−2q)=126
=> 12×(2p−q)=126 [From (i)]
=>2p−q=126 / 12=21 /2 ……… (ii)
From (i) and (ii)
4p=12−21 / 2=32
=>q=38
Putting the value of q in (i)
2p=12−3q=12−3×38
=>2p=(96−9) / 8=87 / 8
=> p = 87 / 16
Now,
p+2q=(87 / 16)+2×3 / 8
=(87+12) / 16=99 / 16
Hence option (4)