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If p:q is the sub duplicate ratio of p-x2:q-x2?
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If p:q is the sub duplicate ratio of p-x2:q-x2?
Explanation of Sub Duplicate Ratio
Sub duplicate ratio refers to a ratio that is obtained by subtracting a fixed number from both the antecedent and consequent of the given ratio. This ratio is also known as subtrahend ratio.


Calculation of p:q sub duplicate ratio
Let p:q be a ratio such that p > q. The sub duplicate ratio of p:q can be calculated as follows:


  • Let x be the fixed number subtracted from both p and q.

  • Then, the sub duplicate ratio of p:q is given by (p-x):(q-x)

  • It can also be written as (p/q - x/q):(q/q - x/q)

  • Further simplifying, we get p:q - x:q



Calculation of p-x2:q-x2 sub duplicate ratio
Let p-x2:q-x2 be a ratio such that p-x2 > q-x2. The sub duplicate ratio of p-x2:q-x2 can be calculated as follows:


  • Let x be the fixed number subtracted from both p and q.

  • Then, the sub duplicate ratio of p-x2:q-x2 is given by (p-x2-x):(q-x2-x)

  • It can also be written as (p/q - (x2+x)/q):(q/q - (x2+x)/q)

  • Further simplifying, we get (p:q - (x2+x)/q):(1 - (x2+x)/q)



Relation between p:q and p-x2:q-x2 sub duplicate ratios
It can be observed that the sub duplicate ratios of p:q and p-x2:q-x2 are related as follows:


  • Let y = x2 + x

  • Then, we have (p-x2):(q-x2) = p:q - x/q

  • Multiplying both sides by q, we get p-qx2:q-qx2 = pq - px

  • Adding yq to both sides, we get p+yq:q+yq = pq + yq - px

  • Dividing both sides by q+yq, we get p/(q+yq):1 = pq/(q+yq) - x/(1+y/q)

  • This implies that the sub duplicate ratio of p:q is related to the sub duplicate ratio of p-x2:q-x2 with x2+x = y as follows:

  • p/(q+yq):1 = (p-x2)/(q-x2+y(q-x2)/q):1

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If p:q is the sub duplicate ratio of p-x2:q-x2?
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If p:q is the sub duplicate ratio of p-x2:q-x2?
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If p:q is the sub duplicate ratio of p-x2:q-x2? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If p:q is the sub duplicate ratio of p-x2:q-x2? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p:q is the sub duplicate ratio of p-x2:q-x2?.
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