Form the linear equations in one variable for the following word problems:

1. One of the numbers is three times the other. Sum of these two numbers are 30. Form the equation to find the numbers using linear equation in one variable.

2. The sum of two consecutive multiples of 5 is 125. Form the linear equation in one variable to find the numbers.

3. The length of a rectangular plot is 5 times its breadth. If the perimeter of the plot is 120 m. Form the linear equation in one variable to find the dimensions of the plot.

4. The length of a rectangular plot exceeds its breadth by 10 m. The perimeter of such a plot is 140 m. Form the linear equation in one variable to find the dimensions of the plot.

5. Two equal sides of an isosceles triangle are each 3 m less than thrice the third side. If the perimeter of the triangle is 123. Then, write the equation in linear equation in one variable to solve for the sides of the triangle.

6. A dealer sold a television set for Rs10,000 and earned a profit of 20%. Find the cost price of the television set.

7. 50 kg of an alloy of lead and tin contains 60% of lead. How much lead must be melted into it to make the alloy contain 75% of the lead?

8. The digit at ten’s place of a two digit number is three times the digit at one’s place. If the sum of this number and the number formed by reversing its digits is 88, form an equation in linear equation in one variable to solve the problem.

9. The sum of two numbers is 2490. If 6.5% of on number is equal to 8.5% of the other. Form an equation in linear equation in one variable to solve for the numbers.

10. The ages of Ramesh and Rahim are in the ratio 5:7. If Ramesh were 9 years older and Rahim 9 years younger, the age of Ramesh would have been twice the age of Rahim. Form an equation in linear equation in one variable to solve for the ages of the two.

11. The distance between two stations A and B is 230 km. two motor cyclists start simultaneously from A and B in the opposite directions and the distances between them after 3 hours is 20 km. if the speed of one motor cyclist is less than that of the other by 10 km/hr. form an equation in linear equation in one variable to solve for their respective speeds.

**Answers:**

1. x + 3x = 30

2. 5x + (5x + 5) = 125

3. 2(2x + x) = 120

4. 2( x + 10 + x)= 140

5. x + (x – 3) + (x – 3) = 123

6. x + 20x/100 = 10,000

7. 3000 + 100x = 3750 + 75x

8. 31x + 13x = 88

9. 65x = 85(2490 – x)

10. 5x + 9 = 2(7x – 9)

11. 3x + 20 + 3(x – 10) = 230

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