If 2s:3t is the duplicate ratio of 2s — p:3t—p then,

a) p²=6st

b)p=6st

c)2p=3st?

Question

If 2s:3t is the duplicate ratio of 2s — p:3t—p then,a) p²=6stb)p=6st c)2p=3st?

Answer

2s-p:3t-p
= p^2/2s×3t
= p^2/6
p^2=6st

Answer

Let's start by simplifying the given ratio:

2s:3t = (2s - p):(3t - p)

We can cross-multiply to find an equation:

(2s)(3t - p) = (2s - p)(3t)

Expanding both sides:

6st - 2sp = 6st - 3pt

Subtracting 6st from both sides:

-2sp = -3pt

Dividing both sides by -2:

p = 3t

Now we can substitute this value for p back into the original ratio:

2s - p:3t - p = 2s - 3t:3t - 3t = 2s - 3t:0

Since the denominator is 0, the ratio is undefined.

Therefore, none of the given options (a), (b), or (c) are true.