Ratio And Proportion Questions

The ratio of the ages of A and B is $3:2$. Ten years hence, the sum of their ages will be $80$. What are their respective present ages (in years)?

If a:b=3:8, find the value of
2a+b
5a−3b
​
.

The ratio of the salaries of S to F is 2:3 and the ratio of their savings is 3:4. What is the ratio of their expenditures if their total savings are equal to the salary of S?

In an army selection process, the ratio of selected to unselected was 3:1. If 60 less had applied and 30 less selected, the ratio of selected to unselected would have been 5:1. How many candidates had applied for the process?

The average age of 4 members of a family is 35 years. Their ages are in the ratio $8:7:1:12$. What is the age of the oldest member of the family (in years)?

The ratio of milk and water in a pot is 3:4. If we add 10 litres milk and 10 litres water, then the ratio becomes 4:5. How much quantity of total mixture was present initially?

In a mixture of milk and water, the ratio of milk to water is $7:3$. If the total mixture is $120\text{litres}$, how many litres of water must be added to the mixture so that the ratio of milk to water becomes $3:2$?

If $P$ and $Q$ are in the ratio $5:6$ and $Q$ and $R$ are in the ratio $14:15$, then $P$ and $R$ will be in the ratio:

If Gaganjyot's salary is
6
7
​
times of Hafiz's and Sayed's is
7
8
​
times of Hafiz's, what is the ratio of Gaganjyot's salary to Sayed's?

If 164 is divided in the ratio 32 : 9, what is the value of the smaller part?

A sum of ₹8,520 is divided between A, B, C and D in the ratio $\frac{1}{2}:\frac{1}{4}:\frac{2}{5}:\frac{5}{8}$. What is the difference between shares of B and D?

If the ratio of $a$ to $b$ is $3:2$ and the ratio of $btoc$ is $8:7$, what is the combined ratio of $a:b:c$?

If A:B=3:5, then what is the value of (A+B):B?

The ratio of speed of $3$ cars are $3:4:6$. What is the ratio of time taken by these cars to cover the same distance?

If A:B=8:13, B:C=5:8 and C:D=4:5, then A:B:C:D is equal to:

A student appeared in $6$ papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of $5:6:7:8:9:10$. Overall he scored $60\%$. In how many papers did he receive less than $60\%$ marks?

A group of 1280 individuals, consisting of teachers and students, is attending a conference. For every 15 students, there is one teacher. How many teachers are in the group?

The ratio of boys to girls in a school having 1440 students is $3:5$. Thirty girls were shifted to the other branch of the school. How many more boys should be admitted to the school to make this ratio $2:3$?

If
b
a
​
=
9
7
​
and
c
b
​
=
5
3
​
, then the value of a:b:c is:

If $5A=13B=7C$, find the value of $A:B:C$.

If 10A=3B=7C; find A:B:C

If the cost of $6$ mangoes is $\text{₹}90$, what is the cost of $10$ mangoes?

The third proportional to 9 and 15 is:

Refer to the data table below and answer the following question:

Four numbers are in the ratio of 2:3:4: 5, and their sum is 56. Find the sum of the first and third numbers.

Directions for Q.55: Study the following description carefully to answer the question.
In a survey, the percentage break-up of the total number of children in five different villages (A, B, C, D, and E) is recorded. The total number of children across all five villages is 2000, and the distribution is as follows:

Village A: 12%

Village B: 16%

Village C: 30%

Village D: 20%

Village E: 22%

What is the respective ratio of the total number of children from village A to village C?

Find the number that must be subtracted from the terms of the ratio $15:19$ to make it equal to $3:4$.

There are two numbers a
2
and 9. Their mean proportion is b, then (a
2
+b
2
):(a
2
−b
2
)=?

If Giridhar's salary is
3
5
​
times of Hariraj's and Shaunak's is
3
2
​
times of Hariraj's, what is the ratio of Giridhar's salary to Shaunak's?

If 25% of X is equal to 40% of Y, then what is the ratio of X and Y?

Three partners decided to start a business. They decided to donate 10% of the profit to a charity organisation and then the remaining profit would be shared among first, second and third partner in the ratio 1: 2: 2. The total profit received was ₹1,80,000. Find the share of the first partner.

The present ages of $A$ and $B$ are in the ratio $15:8$. After $8$ years their ages will be in the ratio $17:10$. What will be the ratio of the ages of $A$ and $B$ after $10$ years from now?

If
Q
P
​
=
S
R
​
=
U
T
​
=
4
3
​
, then what is the value of (4P+5R+7T):(3Q+4S+7U)?

In a farm, in addition to $48$ hens, there are $42$ sheep and $11$ oxen with some shepherds. If the total number of feet is $224$ more than the number of heads, find the number of shepherds.

A sum of ₹ $1518$ is divided among $A,B,$ and $C$, such that $A$ receives $20\%$ more than $B$ and $B$ receives $20\%$ less than $C$. What is the share of $C$ in the sum?

$P$, $Q$, and $R$ are partners in a company. In any given year, $P$ receives $\frac{1}{9}$ part of the total profit, $Q$ receives $\frac{1}{6}$ part of the profit, and $R$ receives $\text{Rs }130000$. How much amount (in $\text{Rs}$) will $P$ get as profit?

In a container, two types of liquids $P$ and $Q$ are in the ratio of $3:7$. If $10$ litres of the mixture is drawn off from the container and it is filled with $6$ litres of liquid $Q$, then the ratio of $P$ and $Q$ becomes $1:3$. What was the original quantity (in litres) of the mixture?

The price of a television set and a washing machine are in the ratio of 8:7. If the cost of the television set is ₹4,800 more than the cost of the washing machine, then find the price of the washing machine.

If $12$, $x$, $8$ and $14$ are in proportion, then what is the mean proportional between $(x-12)$ and $(x+4)$?

Comprehension:The following detailed list shows the results of a survey where $1500$ people exiting voting booths were asked for which party they voted:Party A: $175$ votesParty B: $240$ votesParty C: $375$ votesParty D: $300$ votesParty E: $150$ votesParty F: $120$ votesParty G: $140$ votesWhat is the ratio of voters of party D to voters of party G?

Two vessels $A$ and $B$ contain solutions of acid and water. In $A$ and $B$, the ratios of acid and water are $7:3$ and $4:1$, respectively. They are mixed in the ratio $1:2$. What is the ratio of acid and water in the resulting solution?

The bus fare between two cities is increased in the ratio 1:2. Find the increase in the fare, if the original fare is Rs. 175.

Find the third proportional to 5 and 15 which is equal to the fourth proportional of 2, 5 and 18.

If $x$ is subtracted from each of $17,14,22$ and $18$, then these numbers are in proportion, in this order. What is the mean proportion between $9x$ and $5x$?

Find two numbers such that their mean proportion is 16 and third proportion is 1024.

A sum of $\text{₹}x$ is divided among A, B and C such that the ratio of shares of A and B is $3:4$ and that of B and C is $5:6$. If C receives $\text{₹}1440$ more than what A receives, then the value of $x$ is?

In a $2025\text{ litre}$ mixture of milk and water, the ratio of milk to water is $12:13$. To get a new mixture containing milk and water in the ratio of $12:15$, the amount of water to be added is:

Find the ratio between the fourth proportional of 42, 56, 63 and the fourth proportional of 189, 273, and 153.

Two alloys A and B contain copper and zinc in the ratio $7:2$ and $5:3$ respectively. How many $\text{kg}$ of A and B must be melted in order to get an alloy of $44\text{kg}$ containing copper and zinc in the ratio $3:1$?

If $(2x+3):(5x+4)$ is the triplicate ratio of $3:4$, find the square of $x$.

Three partners, X, Y and Z, shared profits. If the total profit was $\text{Rs. }3,000$, X's share being $\text{Rs. }400$ less than Z's and Y's share being $\text{Rs. }200$ less than Z's, then find the profit sharing ratio of X $:$ Y $:$ Z.

Study the following table, (which shows the number of units of an item manufactured and sold by $5$ companies) and answer the question.CompanyNo. of units Manufactured (in thousands)Sold (in thousands)A4230B4532C3626D5136E5440The ratio of the number of units manufactured by companies C and E together and the number of units sold by A and D together is?

The ratio of speeds of two cars is $10:11$. If the first car travels a distance of $500\text{kms}$ in $10\text{hours}$, what is the speed of the second car?

From the bar graph given in image_9b4085.png, the graph shows the population density of 6 countries. Population density is measured as the number of people living per square kilometre. What is the ratio of the population density of country A to country F?

What is the mean proportional of 45x
4
and 5y
2
?

In an educational institution, the ratio of the numbers of students in middle school and in high school, respectively, in a given year was given as 4: 3. If there were 324 students in middle school in that year in that institution, what was the number of students in high school in the same year in that institution?

If $\frac{x}{y}=\frac{4}{5}$ and $7x+6y=29$, find the value of $y$.

Present ages of Neha and Rashmi are in the ratio of $7:8$ respectively. Six years hence, the ratio of their ages will become $9:10$ respectively. What is Rashmi's present age?

In a mixture of milk and water, the ratio of milk to water is $5:2$. If the total mixture is $35\text{ litres}$, how many litres of milk does it contain?

At the 'Shoot and Win' stall in a fair, $X$ fires $5$ shots to $Y$ 's $3$, but $X$ hits the target only once in three shots while $Y$ hits once in $2$ shots. When $Y$ has missed $27$ times, how many times has $X$ hit his target?

In a certain office, $\frac{1}{3}$ of the workers are women, $\frac{1}{2}$ of the women are married, and $\frac{1}{3}$ of the married women have children. If $\frac{3}{4}$ of the men are married and $\frac{2}{3}$ of the married men have children, what part of the workers are without children?

When 'p' is subtracted from each of 18, 15, 23 and 16, then the numbers so obtained in this order are in proportion. What is the value of (p−14)?

If $39$ candies are to be distributed to A and B in the ratio of $4:9$, how many more candies does B get than A?

The ratio of bus and train fares from Burdwan to a certain place is $3:4$. If the train fare increases by $20\%$ and bus fare by $10\%$, then what will be the new ratio of bus and train fares?

The mean ratio of $11$ and $44$ is ________.

The ratio of two numbers is $5:8$ and their difference is $69$. Find the numbers.

The sum of three numbers is 118. If the ratio of the first number to the second number is 3:4 and that of the second number to the third number is 5:6. Find the third number.

A loss of $\text{Rs. }1,152$ has to be divided among A, B and C in the ratio $7:8:9$, then what is the share of A?

The ratio of two numbers is $3:4$ and their L.C.M. is $180$. Find the numbers.

The sum of the four numbers A, B, C and D is 875. If the ratio of A to B is 1:2, the ratio of B to C is 3:1 and the ratio of C to D is 2:3, find the value of C.

The ages of A and B are in the ratio 4:7, respectively. After 8 years, the ratio of their ages will be 2:3. What is the sum of the present ages of A and B (in years)?

The ratio of three numbers is 3:5:4 and the sum of their squares is 11250. Find the sum of the numbers.

The third proportional of two numbers 9 and 24 is ________.

In a joint business, the ratio of the capitals of three partners is $5:7:9$. If the total profit earned in the business is $\text{Rs. }420$, find the share of the third partner.

In a joint business, the capitals of A and B are in the ratio $3:4$ and the capitals of B and C are in the ratio $6:5$. If A receives a profit share of $\text{Rs. }450$, find the profit share of C.

The ratio of the principal and the amount (principal along with interest) in $1$ year is $8:9$, the rate of simple interest per annum is:

The sum of two numbers is $72$ and their ratio is $2:4$. Find the smallest number among them.

If $\frac{4}{5}:\frac{12}{10}::\frac{x}{6}:\frac{9}{2}$, find the value of $x$.

Find the unknown value of 'x' in the proportion (5x+1):3=(x+3):7

Three partners, A, B and C shared profits in the ratio $4:5:6$. If C's share of the profit was $\text{Rs. }200$ more than that of A, find the total profit generated by them.

The ratio of Bus and Train fare is $4:5$. If the Bus fare increases by $10\%$ and the Train fare increases by $20\%$, the new ratio of Bus and Train fare will be:

If $x:9::5:y$, then $xy=?$

If the ratio of three numbers A, B and C is 2:3:5, and the sum of the squares of these numbers is 3800, then the value of C is:

Three partners, A, B and C shared profits in the ratio $2:3:4$. A new partner D joined who took half of the shares of each A and C. If D's share of profit now is $\text{Rs. }100$, find the total profit.

Find the fourth proportion to $10$, $12$, and $15$.

Find two numbers such that their mean proportion is $12$ and third proportion is $768$.

The bar graph shows information about the sales of wrist watches from five branches $A_1,A_2,A_3,A_4$ and $A_5$ of company 'ABC' in 2016 and 2017.
Let the sales values for $A_2$ be $75$ (in 2016) and $65$ (in 2017), and for $A_4$ be $85$ (in 2016) and $95$ (in 2017).

What is the ratio of total sales of branches $A_2$ and $A_4$ for the year 2016 to the year 2017?

A building which is $64\text{ feet}$ high casts a shadow of length $96\text{ feet}$. Under similar conditions, find the height of a telephone tower which casts a shadow of length $180\text{ feet}$.

Four years ago, the ratio of the ages of A and B was 3: 5. Six years hence, the ratio of the ages of A and B will be 2: 3. What is the sum (in years) of the present ages of A and B?

If $\frac{x}{y+z}=\frac{y}{z+x}=\frac{z}{x+y}=K(K\ne 0)$, then the value of $K$ is:

Two positive numbers are in the ratio 7:11. If the sum of their squares is 13770, then the difference between the two numbers is:

Which of the following ratios is the greatest?

Study the given table and answer the question that follows.
The table shows the percentage population of four states below poverty line and the proportion of male to female.



If the population of states A and D is $18,000$ each, then what is the total number of females below the poverty line in these states combined?

A box contains one red ball, one blue ball and one green ball. The ratio of the weight of the red and blue ball is $5:6$ and that of the blue and green ball is $5:4$. If the blue ball weighs $60\text{g}$, the weight of the green ball is:

$40\%$ of A is $60\%$ of B. $A:B$ will be:

$\text{P}$, $\text{Q}$ and $\text{R}$ enter into a partnership by investing their capitals in the ratio of $\frac{2}{5}:\frac{3}{4}:\frac{5}{8}$. After $4$ months, $\text{P}$ increased his capital by $50\%$, but $\text{Q}$ decreased his capital by $20\%$. What is the share of $\text{Q}$ in the total profit of $\text{₹}28,210$ at the end of a year?

Rs. 9,500 is divided among three friends A, B and C such that B gets 75% of the amount that A gets and the ratio between A and C's shares is 8:5. The amount (in Rs.) that B gets is:

If 5A=12B=13C, find A:B:C.

A bag contains rupee, 50-paise and 25-paise coins in the ratio 3:4:6. If the total amount is ₹143, the number of 50-paise coins is:

If (x+y):(x−y)=5:2, find the value of
x−4y
4x+5y
​
.