Linear Equations Questions

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

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?

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

Find the value of $x$ from the given linear equation:
$$2.75+3.5x=9.25+1.5x$$

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.)?

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.?

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:

Find the value of $m$:
$$m-\frac{2}{3}=\frac{5}{6}+\frac{1}{2}$$

If (x+10)% of 300 is 57.5% more than x% of 250, then 15% of x is what percentage less than 20% of (x+13)?

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

The present ages of Prajwal and Lavanya are in the ratio $5:6$ respectively. After $3$ years, the ratio of Prajwal's age to Lavanya's age will be $6:7$. What is Prajwal's present age?

A certain distance is covered by a car at a uniform speed in $8$ hours. If the speed is reduced by $6\text{km/h}$, it will take $1$ hour more. What is the original speed of the car (in $\text{km/h}$)?

On selling a television at a $6\%$ profit and a fridge at a $9\%$ profit, a shopkeeper gains $\text{Rs. }5,100$. However, if the shopkeeper sells the television at a $9\%$ profit and the fridge at a $6\%$ loss, he gains $\text{Rs. }1,800$ on the whole transaction. The cost price (in $\text{Rs.}$) of the fridge is:

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?

A train can travel $75\%$ faster than a car. Both start from point A at the same time and reach point B, $70\text{km}$ away from A, at the same time. On the way, however, the train lost about $18$ minutes while stopping at the stations. The speed of the car is:

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all 200 questions and scored 500 marks. What is the number of questions he answered correctly?

The average weight of 30 students in a class is 60kg. If the weight of the class teacher is included, the average increases by 0.5kg. The weight (in kg) of the teacher is:

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)?

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?

If 70 is subtracted from 70% of a number, the remainder is 70. What is the number?

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?

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?

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. $x=y$

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

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

Find the value of $V$:
$$25\times 18-660÷30=3V+14$$

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:

If
x+2
2x
​
+
2x+4
1
​
−
2x
2
+4x
12−x
​
=a+
x
b
​
, where a and b are integers, then the value of ab=_____.

If half of a number is equal to two-thirds of 60, find the number.

A group of 6 chairs and 3 tables together has 54 legs. If each chair has 4 legs, how many legs does one table have ?

Find the value of $x$:
$$0.2x+0.04=0.5x-0.11$$

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:

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.

Find the value of $K$ from the given equation:
$$13450+12846-1230-K=23670+987$$

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

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:

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:

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?

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?

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.

$\frac{9}{15}$ 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 $14x+6y-32=0$?

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

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

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

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.:

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

To travel $708\text{km}$, an Express train takes $6\text{ hours}$ more than Rajdhani train. If however, the speed of the Express train is doubled, it takes $3\text{ hours}$ less than Rajdhani train. What is the speed of Rajdhani train?

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 ₹ ______.

An engineering student has to secure $36\%$ marks to pass. He gets $53$ marks and fails by $37$ marks. Find the maximum marks.

Two students appeared for an examination. One of them secured 21 marks more than the other and his marks were 80% of the sum of their marks. The marks obtained by them are:

If the system of linear equations$x+2ay+az=0$$x+3by+bz=0$$x+4cy+cz=0$ has a non-zero solution, then $a,b,c$:

There were two candidates in an election. $10\%$ of voters did not cast their votes. $60$ votes were found invalid. The winning candidate got $47\%$ of the total votes and won by $308$ votes. Find the number of voters enrolled.

The average per day income of A, B and C is $\text{Rs. }45$. If the average per day income of A and B is $\text{Rs. }40$ and that of B and C is $\text{Rs. }43$, then the per day income of B 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 $4200$.

In three containers - yellow, white and black, $120$ marbles are placed. There are twice as many marbles in the white and yellow containers combined as there are in the black container. Also, there are twice as many marbles in the black container as there are in the yellow container. How many marbles are there in the white container?

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?

The average monthly salary of A, B, C and D is ₹$27,200$. A gets ₹$800$ more than B, B gets ₹$600$ more than C, and C gets ₹$400$ more than D. Find the monthly salary of A (in ₹).

The sum of two numbers is 19, while the difference between the two numbers is 3. Find the smaller number out of these two numbers.

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:

The graphs of the lines $x+2y-3=0$ and $2x+4y+11=0$ are

A number exceeds $20\%$ of itself by 60. The number is:

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 value of $K$ for which equation $x-Ky=2$, $3x+2y=5$ has unique solution.