Class 10 CBSE Maths Linear Equations Important Questions
An equation is a statement that two mathematical expressions having one or more variables are equal. Equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.
Q.1 The coach of a cricket team buys 7 bats and 6 balls for ₹13200. Later, he buys 3 bats and 5 balls for ₹5900. Find the cost of each bat and each ball.
Solution
Q2 Taxi charges in a city consist of fixed charges and the remaining depending upon the distance travelled in kilometres. If a person travels 60 km, he pays ₹960, and for travelling 80 km, he pays ₹1260. Find the fixed charges and the rate per km.
Solution
Q3 The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves ₹5000 per month, find the monthly income of each.
Solution
Q4 On selling a TV at 5% gain and a fridge at 10% gain, a shopkeeper gains ₹3250. But, if he sells the TV at 10% gain and the fridge at 5% loss, lie gains ₹1500. Find the actual cost price of TV and that of the fridge.
Solution
Q5 A man invested an amount at 12% per annum simple interest and another amount at 10% per annum simple interest. He received an annual interest of ₹2600. But, if he had interchanged the amounts invested, he would have received ₹140 less. What amounts did he invest at the different rates?
Solution
Q6
The students of a class arc made to stand in rows. If 4 students are extra in each row, there would
be 2 rows less. If 4 students are less in each row, there would he 4 rows more. Find the number of
students in the class.
Solution
Q7
The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
Solution
Q8
If three times the larger of two numbers is divided by the smaller one, we get 4 as the quotient and
3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5
as the quotient and 1 as the remainder. Find the numbers.
Solution
Q9 The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
Solution
Q10
In a given fraction, if the numerator is multiplied by 2 and the denominator is reduced by 5, we get
(6/5). But if the numerator of the given fraction is increased by 8 and the denominator is doubled,
we get (2/5) . Find the fraction.
Solution
Solution
Q11 A man's age is three times the sum of the ages of his two sons. After 5 years, his age will be twice the sum of the ages of his two sons. Find the age of the man.
Solution
Q12
A man travels 370 km, partly by train and partly by car. If he covers 250 km by train and the rest
by car, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18
minutes longer. Find the speed of the train and that of the car
Solution
Q13
A train covered a certain distance at a uniform speed. If the train had been 6 kmph faster, it would
have taken 4 hours less than the scheduled time. And, if the train were slower by 6 kmph, it would
have taken 6 hours More than the scheduled time. Find the length of the journey.
Solution
Q14
A boat goes 16 km upstream and 24 km downstream in 6 hours. Also, it covers 12 km upstream and 36 km
downstream in the same time. Find the speed of the boat in still water and that of the stream.
Solution
Q15 8 men and 12 boys can finish a piece of work in 5 days, while 6 men and 8 boys can finish it in 7 days. Find the time taken by 1. man alone and that by 1 boy alone to finish the work.
Solution
Q16
Find the four angles of a cyclic quadilateral ABCD in which
∠A = (2x - 1)0 , ∠B = (y + 5)0 , ∠C = (2y + 15)0
and ∠D = (4x - 7)0
Solution
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