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
Nice questions👍🏻