Question

If 2s:3t is the dublicate ratio of 2s-p:3t-p then

Answer 1

(2s/3t)² = (2s-p)/(3t-p)
⇒4s²/9t² = (2s-p)/(3t-p)
⇒(3t-p)(4s²/9t²) = (2s-p)
⇒ 3t×(4s²/9t²) - p×(4s²/9t²) = (2s-p)
⇒4s²/3t - p(4s²/9t²) = 2s-p
⇒ p(1- (4s²/9t²)) = 2s - (4s²/3t)
⇒p = (2s - (4s²/3t)) / (1- (4s²/9t²))