Question 1: If , find:

Answer:

Question 2: If , find the value of

Answer:

Question 3: If , find the value of

Answer:

Question 4: If , find the ratio

Answer:

Question 5: If , find the ratio

Answer:

Question 6: If , find the ratio

Answer:

Question 7: Find , when

Answer:

Dividing by

Let

Question 8: If the ratio between 8 and 11 is the same as the ratio of , find the value of

Answer:

Given

Therefore

Question 9: Two numbers are in the ratio 2:3. If 5 is added to each number, the ratio becomes 5:7. Find the numbers.

Answer:

Let the number be . Therefore

Substituting

or

Therefore

Question 10: Two positive numbers are int he ratio of 3:5 and the difference between their squares is 400. Find the numbers.

Answer:

Let the number be

Given

or

Therefore

Question 11: What quantity must be subtracted from each term of the ratio 9:17 to make it equal to 1:3.

Answer:

Let be subtracted. Therefore

or

Question 12: 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 13: The work done by men in days and the work done by men in days are in the ratio . Find the value of .

Answer:

Question 14: The bus fare between two cities is increased in the ratio of . Find the increase in the fare if: i) the original fare is Rs. 245 and ii) the increased fare is Rs. 207.

Answer:

i)

Therefore Increase in the fare

ii)

Original Fare

Therefore Increase in the fare

Question 15: By increasing the cost of the entry ticket to a fair in the ratio of , the number of visitors to the fair has decreased in the ratio of . In what ratio has the total collection increased or decreased.

Answer:

Collections Ratio =

Question 16: In a basket the ratio of the number of oranges and the number of apples is . If 8 oranges and 11 apples are eaten the ratio between the number of oranges and number of apple becomes . Find the original number of oranges and apples in the basket.

Answer:

Substituting

Therefore

Question 17: The ratio between the number of boy sand number of girls in the class is . If there were 20 more boys and 12 less girls, the ratio would have been . Find the total number of students in the class.

Answer:

or

Substituting in i)

Therefore

Hence the total number of students in the class

Question 18: a) If and , find and

b) If and , find

Answer:

a)

Multiplying i) by 6 and ii) by 4 we get

Therefore

Hence

b)

Multiplying i) by 3 and ii) by 2 we get

Therefore

Question 19: If , find

Answer:

Multiplying i) by 6 and ii) by 3 we get

Therefore

For question 20 to 29, please refer to the lecture notes on Ratios and Proportions.

Question 20: Find the compound ratio of

i)

ii)

iii)

iv)

Answer:

i) Compound Ratio of

ii) Compound Ratio of

iii) Compound Ratio of

iv) Compound Ratio of

Question 21: Find duplicate ratio of i) ii)

Answer:

i) Duplicate ratio of

ii) Duplicate ratio of

Question 22: Find triplicate ratio of i) ii)

Answer:

i) Triplicate ratio of

ii) Triplicate Ratio of latex \frac{m}{2}: \frac{n}{3} = \frac{m^3n^3}{216} &s=1$

Question 23: Find sub-duplicate ratio of i) ii)

Answer:

i) The sub-duplicate ratio of

i) The sub-duplicate ratio of latex (x-y)^4:(x+y)^6 = (x+y)^2 : (x+y)^3 &s=1$

Question 24: Find sub triplicate ratio of i) ii)

Answer:

i) The sub-triplicate ratio of

ii) The sub triplicate ratio of

Question 25: Find the reciprocal ratio of i) ii)

Answer:

i) The reciprocal ratio of

ii) The reciprocal ratio of

Question 26: If is the duplicate ratio of , find

Answer:

Question 27: If is the duplicate ratio of ; show that

Answer:

Hence

Question 28: If is the triplicate ratio of , find . [2014]

Answer:

Question 29: Find the ratio compounded of the reciprocal ratio of , the sub – duplicate ration of and the triplicate ratio of .

Answer:

Reciprocal Ratio

Sub Duplicate Ratio

Triplicate Ratio

Compound ratio of the above three

Question 30: If , prove that each of these ratio is equal to provided .

Answer:

Note: if you have