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If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then?
Most Upvoted Answer
If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then?
Explanation:
The duplicate ratio of a:b is (a^2:b^2). Thus, the duplicate ratio of 2s-p:3t-p is ((2s-p)^2:(3t-p)^2).
Solution:
Given, 2s:3t is the duplicate ratio of 2s-p:3t-p.
Thus, we can write (2s)^2:(3t)^2 = (2s-p)^2:(3t-p)^2 (using above explanation)
Expanding the squares, we get:
4s^2:9t^2 = (2s-p)^2:(3t-p)^2
4s^2:9t^2 = 4s^2 - 4sp + p^2 : 9t^2 - 6tp + p^2 (using (a-b)^2 = a^2 - 2ab + b^2)
Cancelling out the common terms, we get:
4sp = 6tp
Dividing both sides by 2p, we get:
2s/3t = 1
Thus, the ratio 2s:3t is equivalent to 2/3.
Conclusion:
Therefore, the duplicate ratio of 2s-p:3t-p is (2/3)^2 : 1^2, which simplifies to 4:9.
The duplicate ratio of a:b is (a^2:b^2). Thus, the duplicate ratio of 2s-p:3t-p is ((2s-p)^2:(3t-p)^2).
Solution:
Given, 2s:3t is the duplicate ratio of 2s-p:3t-p.
Thus, we can write (2s)^2:(3t)^2 = (2s-p)^2:(3t-p)^2 (using above explanation)
Expanding the squares, we get:
4s^2:9t^2 = (2s-p)^2:(3t-p)^2
4s^2:9t^2 = 4s^2 - 4sp + p^2 : 9t^2 - 6tp + p^2 (using (a-b)^2 = a^2 - 2ab + b^2)
Cancelling out the common terms, we get:
4sp = 6tp
Dividing both sides by 2p, we get:
2s/3t = 1
Thus, the ratio 2s:3t is equivalent to 2/3.
Conclusion:
Therefore, the duplicate ratio of 2s-p:3t-p is (2/3)^2 : 1^2, which simplifies to 4:9.
Community Answer
If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then?
P^2=6st
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If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then?
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If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then?.
If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2s : 3t is the duplicate ratio of 2s – p : 3t – p then?.
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