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Syllabus

0.2x + 0.1y = 25

2 (x - 2) - 1.6y = 116

30. A boat sails a distance of 44 km in 4 hours with the current. It takes 4 hours 48minute longer to cover the same distance against the current. Find the speed of boat on still water and the speed of the current.

Please tell question no.9

Q9. The ratio of two numbers is $\frac{2}{3}$. If 2 is subtracted from the first and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

$40.\mathrm{Solve}:\frac{15}{\mathrm{u}}+\frac{2}{\mathrm{v}}=17\mathrm{and}\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}=\frac{36}{5}$

33. A man travels 600km partly by train and partly by car. If he covers 120km by train and the next by car, it takes him 8 hours. But, if he travels 200km by train and the rest by car he takes 20 minutes longer. Find the speed of the car and that of the train.

Q. 2x + 3y = 17

3x - 2y = 6

Q. The sides of an equilateral triangle are (6x + 3y) cm, (8x + 9y - 5) cm and (10x + 12y - 8) respectively. Find the length of each side.

[

Hint.Take 6x + 3y = 8x + 9y - 5 and 8x + 9y - 5 = 10x + 12y - 8 as two equations.](27/8)

^{2/3}- (1/4)^{-2}+ 5^{0}And please explain the sum line by line.

Q.48. 8 men and 12 boys can finish a work in 10 days while 6 men and 8 boys can finish the same work in 14 days. Find the time taken by 1 man and that 1 boy alone to finish the work.

3/x + 4y =7. 5/x + 6y =13

Q.21. A person invested some money at 12 % simple interest and some other amount at 10 % simple interest. He received yearly interest of Rs. 1300. If he had interchanged the amounts, he would have received Rs. 40 more as yearly interest. How much did he invest at different rates?

1=> 0.4x-1.5y=6.5

0.3x+0.2y=0.9

2=> ?2x - ?3y=0

?5x + ?2y=0

Q. 8 The lengths of the sides of the triangle are given in centimetres as:

$\left(2x+\frac{y}{2}\right),\left(\frac{2x}{3}+2y+\frac{5}{2}\right)and\left(y+\frac{5x}{3}+\frac{1}{2}\right).$

If the triangle is equilateral, prove that the triangle whose sides are (2xy+1), (2x+1) and (6y+1) cm each is also equilateral.

Q.50. If twice the son's age in years is added to father's age, the sum is 70. But, if twice the father's age is added to son's age the sum is 95. Find the ages of father and the son.

2x-3y+6=0

2x+3y-18=0

$c)Solvebycrossmultiplicationmethod:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}2x-3y=13;7x-2y=20$

1= The sum of two no.s is 8 and the sum of their reciprocals is 8/15.Find the no.

2=The difference between 2 positive no.s x and y(x>y)is 4 and the difference between their reciprocals is 4/21.Find the no.s

3= The sum of the digits of a two digit no.7.If the digits are reversed, the new no.decreased by 2,equals twice the original no. Find the no.

Q.10. $\frac{2x+1}{7}+\frac{5y-3}{3}=12\phantom{\rule{0ex}{0ex}}\frac{3x+2}{2}-\frac{4y+3}{9}=13$

4x - 3y = -1

Find p, if y = px - 3

Linear Equations by substitutional method

24. A shopkeeper sells a table at 8% profit and a chair at 10% discount, thereby getting Rs. 1008. If he had sold the table at 10% profit and chair at 8% discount, he would have got Rs. 20 more. Find the cost price of the table and the list price of the chair.