Elimination Method of Finding Solution of a Pair of Linear Equations

Q.

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

Q.

A fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator. If $3$ is added to both the numerator and the denominator, it becomes $\frac{5}{6}$. Find the fraction.

Q.

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Q.

Solve for x and y:

$\frac{x}{2}-\frac{y}{9}=6,\frac{x}{7}+\frac{y}{3}=5.$

Q.

Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours. But, if they travel towards each other, they meet in 1 hour. Find the speed of the each car.

Q. A two digit number is obtained by either multiplying the sum of the digits by 8 then subtracting5 or by multiplyimg the difference by 16 and then adding 3 find the number

Q.

Solve the following pair of linear equations by the substitution method.

Q.

The coach of a cricket team buys 7 bats and 6 balls for 3800. Later she buys 3 bats and 5 balls for 1750. Find the cost of each bat and each ball.

Q.

The HCF and LCM of two numbers are $33$ and $264$ respectively. When the first number is completely divided by $2$ the quotient is $33$ the other number is

Q.

The age of father is 3 years more then 3 times the son's age. 3 years hence the, age of father will be 10 years more than twice the age of son. Find their present ages.

Q. Seven times a two digit number is equal to four times the number obtained by reversing the order of the digit. If the sum of the digit is 9, fin the number

Q.

If sum of two numbers is $1215$ and their $\mathrm{HCF}$ is $81$ then , How many such pairs of numbers are possible?

Q.

The monthly incomes of A and B are in the ratio 5:4 and their monthly expenditures are in the ratio 7:5.If each saves Rs.9000 per month, find the monthly income of each.

Q. The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 1250, find their incomes.

Q.

Solve :217x +131y=913

131x+217y=827

Q.

Question 11
If x = a and y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are respectively:
(A) 3 and 5
(B) 5 and 3
(C) 3 and 1
(D) –1 and –3

Q.

The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fractions.

Q.

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days.Find the time taken by one man alone , and that by one boy alone to finish the work.

Q.

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.

Q.

While covering a distance of 30 km.Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.

Q. A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.

Q.

The area of a rectangular plot is 528m. The length of the plot is 1m more than twice its breadth. Find length and breadth.

Q. The income of two persons A and B are in ratio 8:7 And the ratio of their expenditures is 19:16. If their savings are rs2550 per month, find their monthly income.

Q.

Solve for x and y:

$a^{2}x+b^{2}y=c^2,b^{2}x+a^{2}y=d^2.$

Q.

There are two classrooms A and B.If 10 students are sent from A to B, the number of students in each room becomes the same. If 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in each room.

Q.

The sum of the digits of a two-digit number is 15.The number obtained by interchanging the digits exceeds the given number by 9.The number is

(a) 96 (b) 69 (c) 87 (d)78

Q. A father is 3 times as old as his son. In 12 years time, he will be twice as old as his son. Find their present ages.?

Q.

Solve for x and y:

$0.3x+0.5y=0.5,0.5x+0.7y=\mathrm{0.74.}$

Q.

A lending library has a fixed charge for the first three days and additional charge for each day thereafter. Saritha paid $Rs.27$ for a book kept for seven days, while Susy paid $Rs.21$ for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Q.

The students of a class are made to stand in rows. If 4 students are extra in a row there would be 2 rows less. If 4 students less in a row there would be 4 rows more. Find the number of students in the class