Ratio And Proportion Questions

When x is subtracted from each of the numbers 64,81,85 and 109, the numbers so obtained in this order are in proportion. What is the mean proportional between (x+3) and (2x−1)?

A container contains a mixture of milk and water in the ratio $7:5$. When $9\text{litres}$ of mixture is drawn off and the container is filled with water, the ratio of milk and water becomes $7:9$. How many litres of milk was contained by the container initially?

The LCM and HCF of the numbers $42$ and $49$ are in the ratio of

The ratio of milk and water in a mixture is $3:7$. If we add 10 litres of water to the mixture, then the ratio becomes $1:3$. Find the initial quantity of milk.

A, B and C are three numbers. If A exceeds B by 70% and B is 20% less than C, then A : C is:

If $x:4::y:5$, then $x:y$ is:

The ratio of milk and water in a mixture is $3:7$. If we add $10\text{ litres}$ of water to the mixture, then the ratio becomes $1:3$. Find the initial quantity of milk.

The total number of students in three sections A, B and C of a class in a school is 340. The number of students in sections A and B are in the ratio 3:5 and those in sections B and C are in the ratio 3:2. What is the mean proportional between the number of students in section A and the number of students in section C?

If a rope $154\text{ m}$ long is divided in the ratio $9:5$, then the length of the shorter piece (in $\text{m}$) is:

If two numbers are in the ratio
5
4
​
:
6
5
​
, then by what percentage is the first number more or less than the second number?

The fourth proportional to 12,15,24 is:

Eight years ago, the ratio of the ages of $A$ and $B$ was $9:10$. The ratio of their ages $4\text{ years}$ from now will be $12:13$. If the age of $C$ is $4\text{ years}$ less than the present age of $A$, then what is the present age (in years) of $C$?

Raju can complete a piece of job in 15hours, Vinay in 20hours and Vardhan in 30hours. If they work together and they are paid Rs. 7,200 for the job, then what amount would Vinay receive?

Two employees $A$ and $B$ are paid a total of $\text{Rs. }13,455$ per week by their employer. If $A$ is paid $125\%$ of the sum paid to $B$, how much is $B$ paid per week?

In a classroom, the number of boys is three times the number of girls. Which of the following totals cannot represent the number of children in the class?

What is the mean proportional between $2.5$ and $0.625$?

If $5A=6B=9C$, what is $A:B:C$?

In an election, there were three candidates - A, B and C. The winner, A, got five times the votes received by C. B got 240 votes which was 1.5 times the votes of C. How many total votes were polled in the election if there were no bogus votes?

The ratio of cheese to sauce for a single pizza is 1 cup to 1/2 cup. If Rama used 15 cups of sauce to make a number of pizzas, then how many cups of cheese did she use on those pizzas?

6 men earn as much as 7 women, 2 women earn as much as 3 boys, 4 boys earn as much as 5 girls. If 5 girls earn Rs. 400 a week, how much does a man earn in a week?

Out of the total income, a family saves 15% and the rest of the amount is spent on three types of expenditure – health, education and food in the ratio of 1:2:2. The income is Rs. 300 less than thrice the expenditure incurred on education. What is the difference between the savings and the expenditure incurred on health?

Find the third proportional to 6 and 24.

There are Senior officers and Secretaries in an office. If $15\text{ Secretaries}$ went on leave, then every Secretary has two Senior officers. After that $45\text{ Senior officers}$ went on leave and now every Senior officer has $5\text{ Secretaries}$. Then find out how many Secretaries were there initially.

$40$ litres of a mixture contains milk and water in the ratio of $17:3$. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes $7:1$. The quantity of milk added to it was:

What are the current ages of Antony and Betty if their ages are in the ratio $8:9$ now and will be in the ratio $9:10$ four years from now?

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?

The annual incomes of Anand and Bharath are in the ratio 3:5 and their annual expenses are in the ratio 1:3. If each of them saves Rs. 10,000 at the end of the year, then the annual income of Bharath is:

Find the fourth proportion of the following numbers:
3
1
​
rd of 27,
5
4
​
th of 30,
7
3
​
th of 35.

$60$ is the mean proportional of $36$ and $P$. Find the value of $P$.

The ratio of the incomes of A and B is 5: 7 and the ratio of their expenditures is 3: 4. If A and B save ₹5,000 and ₹9,000, respectively, then what is the difference (in ₹) between the income of A and two times the savings of B?

What number will come in place of the question mark?
$$2:5::?:35$$

$57\%$ of Ranita’s weekly income is equal to $76\%$ of Bhaskar’s weekly income. If Ranita’s weekly income was reduced by $\text{₹}400$, while Bhaskar’s weekly income did not change, the ratio of the weekly incomes of Ranita and Bhaskar, respectively, would have been $6:5$. What is Bhaskar’s weekly income (in $\text{₹}$)?

Two numbers A and B are respectively 80% and 50% more than the third number C. What is the ratio of A and B?

The price of a mobile is ₹15,000. During the annual sale, its price decreased in the ratio of 8:5. What is its decreased price (in ₹)?

A sum of Rs. 12,500 is distributed among A, B, C and D such that A gets Rs. 800 more than what B gets, C gets twice of what B gets and D gets Rs. 900 more than what A gets. The ratio in which D, C, B and A receive the sums is:

The three numbers A, B, C are in the ratio
2
1
​
:
3
2
​
:
4
3
​
. The difference between greatest and smallest numbers is 21. The three numbers A, B and C respectively are:

The mean proportion between 5 and 125 is:

The ratio of income of two persons is $10:6$ and that of their expenditures is $18:10$. If they save ₹$5,200$ and ₹$3,600$ respectively, their incomes are:

The following table gives the number of patients visiting a dental clinic for the issues related to their oral health during the months September, October, November and December 2018. Study the table carefully and answer the question that follows.
Month (2018) Filling Root canal Tooth extraction Implants
September 180 480 570 260
October 560 770 620 470
November 940 1080 890 220
December 820 590 530 1040
What is the ratio of the total number of patients in September to the total number of patients in December in 2018?

If
2
a
​
=
3
b
​
=
4
c
​
=
k
2a−3b+5c
​
, then find the value of k.

Two numbers are in the ratio of $3:4$ and their HCF is $88$. Find their LCM.

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

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

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?

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?

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:

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?

$40\text{ litres}$ of a mixture contains milk and water in the ratio of $17:3$. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes $7:1$. The quantity of milk added to it was

What are the current ages of Antony and Betty if their ages are in the ratio $8:9$ now and will be in the ratio $9:10$ four years from now?

A mixture of $750\text{kg}$ of alloy of copper and tin contains $25\%$ tin. How much tin must be added so that it becomes $70\%$ of the mixture?

A varies directly with B. When A=52, B=91. Find the value of A when B=126.

₹5,580 is divided among P, Q and R in the ratio of 7:11:13, respectively. What is the difference (in ₹) between the one-third of the largest share and two-fifth of the smallest?

$\text{A, B and C}$ enter into a partnership by investing a total of $\text{₹ }6,000$. $\text{A}$ invests $\text{₹ }2,000$, while $\text{B and C}$ invest the remaining amount in the ratio of $2:3$ respectively. If the annual profit is $\text{₹ }3,600$, find $\text{C}$ ’s share of the profit.

The sum of the ages of Mary and Jane is $64$. If the ratio of Mary’s age to Jane’s age is $3:5$ respectively, what is Jane’s age?

The mean proportional between 0.012 and 0.027 is:

When $x$ is added to each of $10,23,15$ and $33$, the sums obtained in this order are in proportion. The value of $(x+5)$ is:

There are green, red, and blue marbles in a bag. Their ratio is 5:4:6, respectively. If there are 135 marbles in the bag, what is the difference between the number of blue marbles and that of the red marbles?

The total amount of $49$ is distributed among A, B, and C. A receives $5$ more than B and B receives $4$ more than C. What is the ratio of their shares?

The third proportional to 7
6
1
​
and 11 is:

The mean proportional between $16$ and $49$ is:

If $\text{V}$ is $32\%$ of $\text{H}$, then what percent of $\text{V}$ is $\text{H}$?

In a bag of coloured candies, the ratio of red candies to blue candies is $3:5$ respectively. If there are $24$ red candies, how many blue candies are there?

In 46.5 weeks, Ram raised Rs. 2,170 for science research. How much money will he raise in 30 weeks?

If X and Y have incomes in the ratio 5:3 and expenditures in the ratio 3:1 and each one of them saves ₹27,000, then what is the income of X?

At present, Ritika’s age is 3 times the age of Vipul. After 7 years, Ritika will be 2 times as old as Vipul. What is the present age of Ritika (in years)?

A certain sum is divided among A, B and C in such a way that the ratio of shares of A and B is $3:4$ and that of shares of C and B is $9:5$. If the difference between the shares of A and C is ₹$462$, then the sum (in ₹) is:

There are $35$ girls and $15$ boys in a music club. $10$ new girls join the club. What is the percentage of girls in the club now?

What is n if 16, n and 49 are in continued proportion?

In a street there are 20 dogs and cats. If the ratio between dogs and cats is 3:2, then the number of cats is ________.

What is the sum of the mean proportional between 5 and 9.8 and the third proportional to 7 and 14?

The third proportional of 5 and 15 is:

In an examination, the ratio of practical to theory marks is 3:7. If 80% of the marks are scored in the practical and 60% of marks are scored in the theory, what is the ratio of marks scored in the theory and the practical?

Two numbers are in the ratio of $3:7$. If $11$ is subtracted from each, the ratio between the numbers becomes $7:20$. Find the smaller number.

The ratio of the present age of a father to that of his son is $5:2$. After $5$ years their ages will be in the ratio of $7:3$. The present age of the father is:

The incomes of A and B are in the ratio 3:5 and their savings are ₹14,000 and ₹20,000, respectively. If the ratio of their expenditures is 4:7, then the income (in ₹) of A is:

A factory produces $120$ toys in $8$ days. How many toys will it produce in $15$ days at the same production rate?

A recipe is made using cheese and butter in the ratio 4:3. If Arohi uses 8 bowls of cheese, how many bowls of butter should she use?

The fourth proportional to 10.8, 3.6 and 20.4 is:

In a medical institute, the strength of the students in the first two classes are in the ratio of 8:17. The ratio of the number of students in the second and the third classes is 2:3. What is the average of the number of students in the first and third classes, if the number of students in the second class is 612?

The number of students in three sections of a class in a school are in the ratio 5:7:8. If 20, 25 and 40 more students are admitted in the three sections, respectively, the new ratio becomes 9:12:16. The total number of students after the new admissions is:

What is the reciprocal ratio of 4:5:8?

The fourth proportional to $4$, $a$ and $16a$ is $81$. What is the value of $a$?

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?

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)?

If three partners invest in the ratio $2:3:5$ and share the profit accordingly, then the partner who invests the least will get what fraction of the profit ?

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

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

The third proportional to 9 and 15 is:

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?

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

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?

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?