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?

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).

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

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?

A dealer sells half of the eggs that he has and another half an egg to Anurag. Then he sells half of the balance eggs and another half an egg to Deepak. Then he sells half of the balance eggs and another half an egg to Sivani. In the end he is left with just 7 eggs and he claims that he never broke an egg. How many eggs did he start with?