Question 1: If are in continued proportion, prove that: . [2010]

Answer:

If are in continued proportion, then

Applying componendo and dividendo

Squaring both sides

Substituting

Question 2: Given . Use componendo and dividendo to prove that: . [2010]

Answer:

Given

Applying componendo and dividendo

Simplifying

Square both sides

Applying componendo and dividendo

Simplifying

Question 3: If , find:

i) ii) [2014]

Answer:

i) Given

Applying componendo and dividendo

Simplifying, we get

ii)

Applying componendo and dividendo

Question 4: Using componendo and dividendo, find the value of : [2011]

Answer:

Given

Applying componendo and dividendo

Simplifying

Square both sides

Simplifying we get

Question 5: If , using properties of proportion show that: [2012]

Answer:

Given

Applying componendo and dividendo

Simplify

Now square both sides

Simplifying

or

Question 6: Given, , prove that: [2000]

Answer:

Given

By componendo and dividendo

By Alternendo

Question 7: If , prove that: . [2007]

Answer:

Given

Applying componendo and dividendo

Squaring both sides

Applying componendo and dividendo once again

simplifying

Hence proved.

Question 8: Using the properties of proportion, solve for Given: . [2013]

Answer:

Given

Applying componendo and dividendo

Taking the square root of both sides

Question 9: What least number must be added to each of the numbers to make them proportional. [2005, 2013]

Answer:

Let the number added be

Therefore

Question 10: The monthly pocket money of Ravi and Sanjeev are in the ratio of 5:7 Their expenditures are in the ratio of 3:5. If each saves Rs. 80 per month, find their monthly pocket money. [2012]

Answer:

Let monthly pocket of Rave and Sanjeev by respectively.

Substituting

Substituting

Question 11: If is the triplicate ratio of , find . [2014]

Answer:

Question 12: If , find . [2002]

Answer:

Given

or

Now substituting

Hence

Question 13: The work done by men in days and the work done by men in days are in the ratio . Find the value of . [2003]

Answer:

Amount of work done by men in days

Similarly, amount of work done by men in days

Given

Simplifying

Therefore

Question 14: What number should be subtracted from each of the numbers ; so that the ratios are in proportion. [2004]

Answer:

Let the number subtracted

Therefore

Simplifying

Question 15: is the mean proportion between two numbers and and is the third proportion to and . Find the numbers. [2011]

Answer:

Given is the mean proportion between two numbers

Therefore … … … … … … i)

Also given is the third proportion to

Therefore … … … … … … ii)

Solving i) and ii)

Hence

Hence the numbers are .

Question 16: if , prove that . [2008]

Answer:

Given

or

Applying Componendo and Dividendo

or . Hence proved.