Linear Equations Questions

The sum of two numbers is 450. If the greater number is decreased by 4% and the smaller number is increased by 20%, then the numbers obtained are equal. The smaller number is:

Rishi and Sarita have ₹4,760. If $\frac{9}{16}$ of Rishi's amount is equal to $\frac{3}{4}$ of Sarita's amount, how much does Sarita have?

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)?

The ratio of the sums of money Arun and Ahaan had is $9:5$. If Arun gives ₹$12$ from his share to Ahaan, then the ratio will change to $4:3$. How much money did Arun have initially?

Two students appeared for an examination. One student who scored 20 marks more than the other, his score was 60% of the sum of their marks. What was his score?

There are 100 questions in a question paper, each carrying 2 marks. But there is a negative marking. 1 mark is deducted for each question answered incorrectly. A student answering all the questions got 80 marks. The number of questions correctly answered by him is

In an enclosure, there are crows as well as cows. If there are 30 heads and 100 legs, what is the ratio of the cows to crows?

Given the simultaneous linear equations $2x-3y=-12$ and $\frac{x}{y}=\frac{3}{4}$, what are the values of $x$ and $y$?

For what value of $p$ does the system of equations $18x+36y+45=0$ and $px-54y+67=0$ have no solution?

What is the solution to the following system of linear equations?
$$3x-9y+4z=5$$
$$2x+7y+z=12$$
$$3x-z=0$$

A company is manufacturing three different products – Glass, Plate and Bowl. The number of Plates is double the number of Glasses. The number of Glasses manufactured is twice the number of Bowls. What is the difference between the number of Plates and the number of Bowls if the total units manufactured by the company is $2380$?

When 44 is subtracted from a number; it reduces to its 60%. Three-fifth of that number is:

The average weight of X and Y is 40kg. The average weight of Y and R is 62kg and the average weight of X and R is 56kg. The weight of X is:

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?

A farmer covered a total distance of $70\text{km}$ in $10\text{hours}$. He travelled part of the distance on foot at a speed of $5\text{km/h}$ and the remaining distance by bicycle at a speed of $10\text{km/h}$. Find the distance travelled on foot.

If $(0,0)$, $(4,-3)$ and $(x,y)$ are collinear then

Total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders are $120$ and $100$, the total expenses are $\text{Rs. }2000$ and $\text{Rs. }1700$ respectively. Find the total number of boarders if the total expense is $\text{Rs. }1880$.

A contractor employed $100$ labourers, both male and female. Each female labourer receives $\text{Rs. }144$ as daily wages while each male labourer receives $\text{Rs. }96$ as daily wages. If the contractor distributes $\text{Rs. }12,480$ daily as wages, how many more female labourers did he employ than male labourers?

Rohan appeared for the Global Talent Search Examination wherein $4$ marks are awarded for every correct answer and $1$ mark is deducted for every wrong answer. Rohan attempted all the $60$ questions and secured $130$ marks. What would have been his score if there was no negative marking?

If $35\%\text{ of }200+\sqrt{x}=48\%\text{ of }550-10\%\text{ of }150$, then $x$ is equal to:

Total price of $6\text{ shirts}$ and $7\text{ trousers}$ is $\text{Rs. }4,130$ while that of $4\text{ shirts}$ and $9\text{ trousers}$ is $\text{Rs. }4,270$. Find out the price of $3\text{ shirts}$.

If a man runs $6\text{kmph}$ from his house, he misses the train at the station by $8\text{ minutes}$. If he runs at $10\text{kmph}$, he reaches the station $7\text{ minutes}$ earlier than the departure of the train. What is the distance of the station from his house (in $\text{km}$)?

Ram was asked to find $\frac{7}{8}$ of a fraction but he mistakenly divided the fraction by $\frac{7}{8}$. As a result, the difference between the answers was $\frac{75}{784}$. What should be Ram’s correct answer?

$\text{Rs. }6000$ is divided among $40$ boys and some girls so that each boy gets $\text{Rs. }100$ and each girl gets $\text{Rs. }250$, then the number of girls is:

Free books were distributed equally among children of a class. The number of books each child got was one-eighth of the number of children. Had the number of children been half, each child would have got $16$ books. How many books were distributed in total?

A cricket team won $3$ matches more than they lost. If a Win gives them $2$ points and Loss $(-1)$ point, how many matches, in all, have they played if their score is $23$?

The sum of three consecutive multiples of $3$ is $72$. What is the largest number among them?

Total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders is $120$ and $100$, the total expenses are $\text{Rs. }2000$ and $\text{Rs. }1700$ respectively. Find the total number of boarders if the total expense is $\text{Rs. }1880$.

The two equations $3x+6y=15$ and $6x+12y=30$ have

In a two digit number, the unit's digit exceeds ten's digit by $2$ and the product of the sum of the digits and the number itself is $144$, then what is the number?

If 2x+3y=0 and 3x−4y=34, then x−y=____.

The age of a father is twice that of his elder son. Ten years hence, the age of the father will be three times that of his younger son. If the difference between the ages of the two sons is $15\text{years}$, the current age of the father is:

The total price of $6$ shirts and $7$ trousers is $\text{Rs. }4,130$ while that of $4$ shirts and $9$ trousers is $\text{Rs. }4,270$. Find out the price of $3$ shirts.

A farmer has some hens and some rabbits. If the total number of the feet of the hens and the rabbits is $160$ and their total number of heads is $50$, the number of hens the farmer has is:

Mohit went to a shop to buy $50\text{kg}$ of rice. He buys two varieties of rice which cost him $\text{Rs. }4.50$ per kg and $\text{Rs. }5$ per kg. He spends a total of $\text{Rs. }240$. What was the quantity of less expensive rice bought by him?

Satyajit is younger than Diganta by $8$ years. If their ages are in the ratio of $5:7$, then how old is Satyajit?

The age of a son today is ${\frac{1}{4}}^{\text{th}}$ of the age of his father. After $20$ years, the age of the father will be twice the age of his son. The age of the father today is:

In an election, $15\%$ of voters did not cast their votes. Ratanbabu got $62.5\%$ of the votes cast and was declared elected by a majority of $3400$ votes. Find the total number of voters.

Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

Three times the first of three consecutive odd integers is $3$ more than twice the third. The third integer is:

A boat running downstream covers a distance of $16\text{km}$ in $2\text{hours}$ while for covering the same distance upstream, it takes $4\text{hours}$. What is the speed of the boat in still water?

In a certain examination, a candidate answered $25$ questions and two-fifth of the rest of the total number of questions, and he found that he has answered only $60\%$ of the total number of questions. How many questions did he answer?

Total price of $6$ shirts and $7$ trousers is $\text{Rs. }4,130$ while that of $4$ shirts and $9$ trousers is $\text{Rs. }4,270$. Find out the price of $3$ shirts.

A man deposited $\text{Rs. }3,000$ in a Bank and $\text{Rs. }2,500$ in a Post Office. The rate of interest of the Bank is $\frac{1}{2}$ more than that of the Post Office. If he gets $\text{Rs. }235$ as total interest at the end of the year, the rate of interest of the Post Office is:

The incomes of $A$ and $B$ are in the ratio $3:2$ and their expenditures are in the ratio $5:3$. If each individual manages to save $\text{Rs. }1,000$, then $B$ 's income is:

There are $100$ questions in a question paper, each carrying $2$ marks. There is a negative marking of $1$ mark deducted for each question answered incorrectly. A student answering all the questions got $80$ marks. Find the number of questions correctly answered by him.

A man travels $800\text{ km}$ partly by rail and partly by steamer. He spends $7\text{ hours}$ more time on the steamer. If the velocity of the steamer is $20\text{ km/hr}$ and the velocity of the rail is $55\text{ km/hr}$, how much distance does he cover by steamer?

A teacher travelled a distance of 22km in 7 hours. He travelled partly on foot at the speed of 2km/h and partly on bicycle at the rate of 4km/h. The distance travelled on foot is:

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?

Sudha decide to donate 12% of her monthly income to an orphanage. On the day of donation, she changed her decision and donate a sum of Rs. 3,600, which was equal to 60% of what she had decided earlier. What is her monthly income (in Rs.)?

The average of the ages of A and B is 25 years, that of B and C is 30 years and that of C and A is 32 years. The age of C (in years) is:

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)?

Dinesh is travelling on his bike. He will reach point P at 6 p. m. if he travels at 20 km/h. He will reach point P at 2 p. m. if he travels at 30 km/h. At what speed must he travel to reach point P at 4 p. m.?

In a Panchayat election, three contestants - A, B, and C - are contesting. 75% of the total population of 8000 cast their votes. There were no invalid or NOTA votes in the election. A got the least votes, with only 300 votes. B got 66% of the total votes and won the election. How many votes did B get?

In a college election between two rivals, a candidate got 30% of the total votes polled. He was defeated by his rival by 200 votes. The total number of votes polled was:

Mr Gogia invested an amount of ₹13,900 divided into two different schemes A and B at the simple interest rate of 14%p.a. and 11%p.a., respectively. If the total amount of simple interest earned in 2 years is ₹3,508, what was the amount invested in scheme B?

The average monthly income of A and B is $₹1400$, that of B and C is $₹1560$ and of A and C is $₹1440$. The monthly income of C is

After $60$ years, Hardik's age will be seven times the age he was $6$ years ago. What is his present age?

If $70\%$ of a number is $56$, what is the value of the number after increasing it by $25\%$?

Read the question and statements provided and then decide whether the information provided in the statements is sufficient to answer the question.
Find the unique values of $x$, $y$ and $z$, if:
Statements:
I. $2x+3y+z=16$
II. $x=y$

The average cost of a pencil is ₹8 and the average cost of an eraser is ₹4. The cost of 8 erasers, 4 pencils and 12 sharpeners are ₹148. The average cost of a sharpener is ₹ ______.

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.

A few students went on a trip and the total amount planned to be spent was $\text{₹}96$. However, $4$ students did not turn up and as a result the remaining students had to contribute $\text{₹}4$ extra. The number of students who attended the trip was:

The average monthly income of $A$ and $B$ is $\text{Rs. }1400$, that of $B$ and $C$ is $\text{Rs. }1560$ and of $A$ and $C$ is $\text{Rs. }1440$. The monthly income of $C$ is:

The Venn diagram shows the number of people who bought ice-cream and drinks in a theatre. Ice-cream is sold for INR 3 and drinks are sold for INR 2. A total of INR 262 is spent. How many people bought both a drink and an ice-cream?

If the average of $46,x,30,36,59,82,68,$ and $94$ is $56.5$, then what is the value of $x$?

A, B and C subscribe to a business of $\text{Rs. }50,000$. B subscribes $\text{Rs. }6,000$ more than C and A subscribes $\text{Rs. }2,000$ more than B. What will be A's share of profit out of a total profit of $\text{Rs. }10,000$?

X travelled a distance of $75\text{km}$ in $8$ hours. He travelled partly by foot @ $5\text{km/h}$ and partly on bicycle @ $12\text{km/h}$. Find the distance that X covered on foot.

A lady said, "If you reverse my age digits, you'll get my husband's age. He is older, and the difference between their ages is one-eleventh of their sum." What is the man's age?

If $7\%$ of S.P. is equal to $8\%$ of C.P. and if $9\%$ of S.P. is $\text{Rs. }2$ more than $10\%$ of C.P, then find C.P. and S.P.:

The value of x for which the expressions 15−7x and 15x+7 become equal is ________.

A hunter was asked how many birds he had caught and had in his bag. He replied that there were all parrots but eight, all ducks but eight, and all swans but eight. How many birds did he catch in total?

$\frac{9}{15}$ of $\frac{7}{3}$ of a number is greater than $\frac{7}{12}$ of $\frac{3}{5}$ of the same number by $7$. Find twice the number.

How many solutions will a pair of linear equations have, if the equations are $7x+4y-16=0$ and $14x+6y-32=0$?

Two chairs and a table can be bought for $\text{Rs. }170$. Five chairs and four tables can be bought for $\text{Rs. }530$. Find the cost of a chair.

The sum of two numbers is $80$ and their difference is $8$. What is the ratio of the two numbers?

With a uniform speed, a car covers a distance in 16 hours. Had the speed been increased by 20km/h, the same distance would have been covered in 12 hours. The total distance covered by the car is:

In triangle $PQR$, the length of side $QR$ is less than twice the length of side $PQ$ by $3\text{cm}$. The length of side $PR$ exceeds the length of side $PQ$ by $14\text{cm}$. If the perimeter is $55\text{cm}$, find the length of the smallest side of the triangle $PQR$.

Determine the value of $x$ if $30\%$ of $4200+35\%$ of $2400=x\%$ of $4200$.

The cost of a mango is 8 each, while a guava costs 6 each. A woman spends a total of 52 on these fruits. How many mangoes and guavas did she buy?

There are 1550 boys and girls in a school. The number of girls exceeds the number of boys by 500. What is the percentage (to the nearest integer) of girls in the school?

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: