Linear Equations Questions with Solutions

Runs scored by Sachin in a charity match are 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together, they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?

An examination consists of 160 questions. One mark is given for every correct option. If $\frac{1}{4}$ mark is deducted for each wrong option and half a mark is deducted for each unanswered question, a student scores 79. If half a mark is deducted for every wrong option and $\frac{1}{4}$ mark for every unanswered question, the student scores 76. Find the number of correct answers he wrote.

X, Y, W, Z jointly purchased an office space for Rs 84 lakhs. The amount contributed by Y, W and Z put together is three times that of X. The amount contributed by X, W and Z put together is 320% of Y. Further, the amount contributed by W is 20% of X, Y and Z put together. What is the contribution of Z?

Five years ago, A was three times as old as B. Now, A is twice as old as B. What is A's current age in years?

Birds on trees $A$ and $B$ say: if $2$ from $B$ move to $A$, numbers are equal; if $2$ from $A$ move to $B$, then $B$ becomes double of $A$. Find numbers on $A$, $B$.

On Monday, Akash ran 4 km less than the distance he ran on Tuesday. Sanjay, who ran the same distance on Monday and Tuesday, ran 5 km more on Tuesday than the distance Akash ran on Monday. Find the difference between the distances covered by Akash and Sanjay over the two days.

Rakesh says to Mahesh, "I am as old as you were when I was one-third as old as you are." If the sum of their ages is 60 years, find the present age of Mahesh (in years).

When Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when he was born?

The number of values of $k$ for which the system of equations $\left(k+1\right)x+8y=4k$ and $kx+\left(k+3\right)y=3k-1$ has infinitely many solutions, is

Pushpa is twice as old as Rita was two years ago. If the difference between their present ages is $2$ years, how old is Pushpa today?

Reena met Natasha's children. Rahul said, "The square of my age plus the cube of my sister's age is 7148." Preeti said, "The square of my age plus the cube of his age is 5274." What are the ages of Preeti and Rahul?

Bala had three sons. He had some chocolates which he distributed among them. To his eldest son, he gave 3 chocolates more than half the number of chocolates with him. To his second son, he gave 4 chocolates more than one third of the remaining chocolates. To his youngest son, he gave 4 chocolates more than one fourth of the remaining chocolates. He was left with 11 chocolates. How many chocolates did he have initially?

There were a total of $10$ bicycles and tricycles. If the total number of wheels was $24$, how many tricycles were there?

A person's present age is two-fifth of the age of his mother. After 8 years, he will be one half of the age of his mother. What is the present age of the mother?

A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations make a sum of Rs. 12450. The number of Rs. 20 notes is

Radha is twice as old as Rita was 2 years ago. If the difference between their ages is 2 years, how old is Radha today?

The sum of ages of a daughter and mother is 63 years. Four years back, the mother's age was 4 times that of daughter's age at that time. What is the present age of the mother?

John is 20 years older than Steve. In 10 years, Steve's age will be half of that of John. What is the present age of Steve?

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77, but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

My mother is twice as old as my brother. I am five years younger than my brother but three years older than my sister. If my sister is twelve years of age, how old is my mother?