Linear Equations Questions with Solutions

23 questions15 easy8 medium

A linear equation is an equation in which each variable appears only to the first power, such as 3x + 2y = 12. This topic covers solving equations in one variable, solving pairs of equations in two variables by substitution or elimination, conditions for unique, infinite or no solutions, and turning word problems into equations. Typical word problems involve ages, numbers and their digits, ticket and fruit prices, and fractions. The most important skill is translating the sentence correctly into an equation. In multiple-choice questions, substituting the answer options back into the equations is often faster than solving from scratch. Practise the linear equation questions below. Each solution shows how to form the equation from the question and solve it step by step.

All Questions Easy Medium Hard

Q1.
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?
A. 20B. 15C. 25D. 30
easyAsked in NIMCET 2026View solution ›
Q2.
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 $A$ , $B$ .
A. $8, 12$ B. $10, 14$ C. $14, 10$ D. $5, 7$
easyAsked in MAH MCA CET 2025View solution ›
Q3.
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.
A. 4 kmB. 6 kmC. 5 kmD. 9 km
easyAsked in NIMCET 2023View solution ›
Q4.
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?
A. 15 yearsB. 14 yearsC. 7 yearsD. 10 years
easyAsked in NIMCET 2013View solution ›
Q5.
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?
A. $6$ yearsB. $8$ yearsC. $10$ yearsD. $12$ years
easyAsked in NIMCET 2011View solution ›
Q6.
There were a total of $10$ bicycles and tricycles. If the total number of wheels was $24$ , how many tricycles were there?
A. $4$ B. $6$ C. $8$ D. $2$
easyAsked in NIMCET 2008View solution ›
Q7.
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. 40B. 30C. 60D. 50
easyAsked in NIMCET 2020 +1View solution ›
Q8.
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
A. 200B. 144C. 125D. 110
easyAsked in NIMCET 2020View solution ›
Q9.
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?
A. 6B. 8C. 10D. 12
easyAsked in NIMCET 2021View solution ›
Q10.
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?
A. 46 yearsB. 48 yearsC. 50 yearsD. 59 years
easyAsked in NIMCET 2014View solution ›
Q11.
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?
A. 2B. 8C. 10D. 20
easyAsked in NIMCET 2017View solution ›
Q12.
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?
A. Rs. 4, Rs. 23B. Rs. 13, Rs. 17C. Rs. 15, Rs. 14D. Rs. 17, Rs. 13
easyAsked in NIMCET 2018View solution ›
Q13.
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?
A. 24B. 30C. 40D. 50
easyAsked in NIMCET 2018View solution ›
Q14.
In which year was Arjun born? Arjun at present is 25 years younger than his mother. Arjun's brother, who was born in 1964, is 35 years younger than his mother.
A. 1974B. 1964C. 1944D. 1954
easyAsked in NIMCET 2024View solution ›
Q15.
Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3 : 2. What is Ram's present age?
A. 60B. 40C. 70D. 50
easyAsked in NIMCET 2025View solution ›