Solving Linear Equation by Transposition Method

Q.

A Bag contains white and black balls. Half the number of white balls is equal to one third of the number of black balls. Twice the total number of balls exceeds three times the number of black balls by$4$. How many balls of each colour does the bag contain?

Q. Solve, $\frac{x-4}{3}+\frac{2x-3}{35}=\frac{5x-32}{9}-\frac{x+9}{28}$.

1. 19
2. 5
3. 10
4. 20

Q. A person walks 5 km, then travels a certain distance by train, and then travels by bus which is equal to thrice the distance travelled by train. If the distance covered in whole journey is 65 km, then find the distance travelled by train.

1. 25 km
2. 30 km
3. 15 km
4. 20 km

Q. The altitude of a triangle is two-fifth the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, then the area of the triangle remains the same. Find the base of the triangle in cm.

Q. $3x-9=36$
Solve for the value of x.

1. 10
2. 9
3. 15
4. 12

Q. Ankan bought a pizza and cut it into three pieces. He found the first piece is 5 g ligher than the second piece. He also found that the third piece is four times heavier than the second piece. If the whole pizza weighed 355 g, then find the weight of the three pieces.

1. 55 g, 60 g, 240 g
2. 25 g, 30 g, 120 g
3. 35 g, 40 g, 160 g
4. 30 g, 35 g, 140 g

Q. $\frac{x}{4}+2=10$

Solve for the value of x.

1. 10
2. 40
3. 22
4. 32

Q. $2x+5=25$
Solve for the value of x.

1. 10
2. 20
3. 15
4. 25

Q. A test consists of 60 multiple choice questions. 3 marks are given for each correct answer and 1 mark is deducted for each wrong answer. If Vinita attempted all questions and scored 60 marks, then how many questions did she attempt correctly?

1. 35
2. 40
3. 30
4. 25

Q. Find x and m
(i) $\frac{3x-2}{4}$ - $\frac{(x-3)}{5}$ = - 1

(ii) $\frac{m+9}{3m+15}$= $\frac{5}{3}$
[2 marks]

Q. Solve $\left\{3\right(2x-5)-7\}\ge 9(x-5)$.

Q.

The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, sum of their ages will be 70 years. Find their present ages.

1. 10 years, 30 years

2. 15 years, 45 years

3. 20 years, 60 years

4. 18 years, 54 years

Q. There are 40 passengers in a bus. Some have tickets worth ₹ 3 and remaining worth ₹ 10. The total collection from these passengers is ₹ 295. Find how many passengers have tickets worth ₹ 3.

1. 23
2. 19
3. 15
4. 11

Q. The distance between two milestones is 230 km and two cars start simultaneously from the milestones in opposite directions. The distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/hr, then find the speed of each car.

1. 25 km/hr, 40 km/hr
2. 40 km/hr, 50 km/hr
3. 20 km/hr, 40 km/hr
4. 40 km/hr, 30 km/hr

Q. The value of x in 2x-2= x is 2.

1. False
2. True

Q. The equations 2x+5= x+8 and 7x+7=6x+10 have same solution.

1. False
2. True

Q. The total number of boys and girls in a class is 60. If the number of girls is 10 more than boys, then how many boys and girls are there in the class?

1. 25 boys and 35 girls
2. 35 boys and 25 girls
3. 20 boys and 30 girls
4. 40 boys and 20 girls

Q. Solve $2x+5=3(x+2)$ for $x$.

1. -1
2. 3
3. 1
4. -2