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If 2s:3t is the duplicate ratio of 2s-p:3t-p then
- a)p2=6st
- b)p=6st
- c)2p=3qy
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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If 2s:3t is the duplicate ratio of 2s-p:3t-p thena)p2=6stb)p=6stc)2p=3...
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If 2s:3t is the duplicate ratio of 2s-p:3t-p thena)p2=6stb)p=6stc)2p=3...
Given: 2s:3t is the duplicate ratio of 2s-p:3t-p
To find: Value of p
Solution:
Duplicate ratio means the ratio of the ratio is equal to the given ratio.
So, (2s-p):(3t-p) is the duplicate ratio of 2s:3t, then
(2s-p):(3t-p) = (2s:3t)^2
(2s-p):(3t-p) = (2s)^2:(3t)^2
(2s-p):(3t-p) = 4s^2:9t^2
Cross-multiplying
9t^2(2s-p) = 4s^2(3t-p)
18st^2 - 9tp = 12s^2t - 4p s^2
Collecting like terms
18st^2 - 12s^2t = 9tp + 4p s^2
6st(3t-2s) = p(9t+4s^2)
p = 6st(3t-2s)/(9t+4s^2)
p = 2s(3t-2s)/ (3t+4s^2/9t)
p = 2s(3t-2s)/ (3t/9t+4s^2/9t)
p = 2s(3t-2s)/ (1/3 + 4s^2/9t)
p = 6st(3t-2s)/ (1+4s^2/3t)
p = 6st(3t-2s)/ (3t+4s^2)
p = 6st/(3t+4s^2) * (3t-2s)
p = 6st*3t-6st*2s/ (3t+4s^2)
p = 18st-12s^2t/ (3t+4s^2)
p = 6st(3-2s/ (3t+4s^2)
Therefore, option (a) p = 6st(3-2s/ (3t+4s^2) is the correct answer.
To find: Value of p
Solution:
Duplicate ratio means the ratio of the ratio is equal to the given ratio.
So, (2s-p):(3t-p) is the duplicate ratio of 2s:3t, then
(2s-p):(3t-p) = (2s:3t)^2
(2s-p):(3t-p) = (2s)^2:(3t)^2
(2s-p):(3t-p) = 4s^2:9t^2
Cross-multiplying
9t^2(2s-p) = 4s^2(3t-p)
18st^2 - 9tp = 12s^2t - 4p s^2
Collecting like terms
18st^2 - 12s^2t = 9tp + 4p s^2
6st(3t-2s) = p(9t+4s^2)
p = 6st(3t-2s)/(9t+4s^2)
p = 2s(3t-2s)/ (3t+4s^2/9t)
p = 2s(3t-2s)/ (3t/9t+4s^2/9t)
p = 2s(3t-2s)/ (1/3 + 4s^2/9t)
p = 6st(3t-2s)/ (1+4s^2/3t)
p = 6st(3t-2s)/ (3t+4s^2)
p = 6st/(3t+4s^2) * (3t-2s)
p = 6st*3t-6st*2s/ (3t+4s^2)
p = 18st-12s^2t/ (3t+4s^2)
p = 6st(3-2s/ (3t+4s^2)
Therefore, option (a) p = 6st(3-2s/ (3t+4s^2) is the correct answer.
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Community Answer
If 2s:3t is the duplicate ratio of 2s-p:3t-p thena)p2=6stb)p=6stc)2p=3...
Divide second equation by -2 and you will see both are parallel to each other hance won't intersect and no solution
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