Question 1: Express the following ratios in simplest form:

i) ii) iii) iv) v) vi)

Answer:

i)

ii)

iii)

iv)

v)

vi)

Question 2: Express the following ratios in simplest form:

i) ii)

iii) iv)

v)

Answer:

i)

ii)

iii)

iv)

v)

Question 3: Which ratio is greater:

i) ii)

iii) iv)

Answer:

i) . Therefore is greater than

ii)

Therefore is greater than

iii)

Therefore is greater than

iv)

Therefore is greater than

Question 4: Arrange the following ratios in ascending order of magnitude:

i) ii) and

Answer:

i)

Therefore

ii) and

Therefore

Question 5: Divide Rs. between and in the ratio

Answer:

A’s Share Rs

B’s share Rs

Question 6: Divide Rs. among A, B, C in the ratio of

Answer:

A’s share Rs

B’s share Rs

C’s share Rs

Question 7: Divide Rs. among A, B, C in the ration of

Answer:

A’s share Rs

B’s share Rs

C’s share Rs

Question 8: Divide Rs. between and in the ratio

Answer:

A’s share Rs

B’s share Rs

Question 9: Divide Rs. among such that

Answer:

A’s share Rs

B’s share Rs

C’s share Rs

Question 10: A big contains one rupee, p and p coins in the ration of amounting to Rs . Find the number of coins in each type.

Answer:

Coins: One Rupee paisa paisa

Amount: One Rupee paisa paisa

Therefore

Therefore the coins are in ratio of or

Question 11: Find when:

i) and

ii) and

iii)

Answer:

i) and

and

LCM of and . Therefore we can say

Therefore

ii) and

and

LCM of and . Therefore we can say

Therefore

iii)

and

LCM of and . Therefore we can say

Therefore

Question 12: If and , find and .

Answer:

Therefore,

Now, and

LCM of and , Therefore we can say

Therefore

Question 13: If and , find and

Answer:

Therefore,

Now, and

LCM of and , Therefore we can say

Therefore

Question 14: Two numbers are in the ration of . On adding to the first and to the second, their rations become . Find the numbers.

Answer:

Let the two numbers be and . Therefore

or

Question 15: A sum of money is divided between and in the ratio . If B’s share is Rs. , find the total amount.

Answer:

Let the total money to be divided be

Rs.

Question 16: Two numbers are in the ratio of . If their difference is , find the numbers.

Answer:

Let the two numbers be and

Given or and

Substituting

Question 17: A certain sum of money is divided between and in the ration of . If A’s share is Rs. , find the total amount and also the shares of each one of and .

Answer:

Let the total money to be divided be

Rs.

B’s share Rs.

C’ s share Rs.

Question 18: The ratio of the number of boys and number of girls in a school of students is . If new boys are admitted, find how many new girls can be admitted to make the ratio .

Answer:

Let the number of boys and girls be and respectively.

or

hence

Let the number of girls added

Solve for . Therefore we need to add girls to make the new ratio to

Question 19: The sum of three numbers is . If the ratio of the first to the second is and that of the second to the third is , then find the numbers.

Answer:

Let the three numbers be and .

LCM of and is .

Therefore

Therefore

Hence:

Question 20: Find the number which when added to each term of the ratio , changes the ratio to

Answer:

Let be added to both the terms

Question 21: The present ages of Mr. X and his Son are in the ratio of . If the ratio of their ages years ago was , then find their present ages

Answer:

Let the present age of Mr. X be and his son be . Therefore

or

Solving for and

Question 22: Salaries of and are in the ratio of . If the increment of and are allowed respectively in their salaries, then what will be the new ratio of their salaries.

Answer:

If A’s salary was , B’s salary was and C’s salary was , then the ratios of their salaries would be .

With increments, A’s salary becomes , B’s salary becomes and C’s salary becomes .

Therefore the new ratio would be

Question 23: A got marks out of in Physics and marks out of in Math. In which of the two subjects did he perform better?

Answer:

LCM of and Therefore

Therefore A performed better in Math.

Question 24: A mixture consists of only two components and . In liters of this mixture, the components and are in the ratio of . What quantity of component B $ has to be added in this mixture so that the new ratio is ?

Answer:

Quantity of in the mixture liters

Quantity of in the mixture liters

Let the quantity of added to the mixture is

or liters