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)?

A student made twice as many mistakes as he got correct answers. If he attempted $48$ questions in total, how many questions did he get right?

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?

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 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?

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.

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 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?

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?

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:

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?