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Let the speed of the train and bus be u and v respectively Now According to the question, And Let,  Now, our equation becomes And By Cross Multiplication method, And Hence, Hence the speed of the train and bus are 60 km/hour and 80 km/hour respectively.
Let the number of days taken by woman and man be x and y respectively, The proportion of Work done by a woman in a single day The proportion of Work done by a man in a single day  Now, According to the question, Also,   Let,  Now, our equation becomes And By Cross Multiplication method, So,
Given Equations, As we can see by adding and subtracting both equations we can make our equations simple to solve.  So, Adding (1) and )2) we get, Subtracting (2) from (1) we get, Now, Adding (3) and (4) we get, Putting this value in (3)    Hence, .
Given, And Now, Subtracting (1) from (2), we get Substituting this in (1), we get, . Hence,
Given equation, Now By Cross multiplication method,
Given Two equations,  Now By Cross multiplication method,
Given Equations, Now By Cross multiplication method,
As we know that in a quadrilateral the sum of opposite angles is 180 degree. So, From Here, Also, Multiplying (1) by 3 we get, Now, Subtracting, (2) from (3) we get, Substituting this value in (1) we get, Hence four angles of a quadrilateral are :
Given two equations, And Points(x,y) which satisfies equation (1) are: X 0 1 5 Y -5 0 20 Points(x,y) which satisfies equation (1) are: X 0 1 2 Y -3 0 3   GRAPH: As we can see from the graph, the three points of the triangle are, (0,-3),(0,-5) and (1,0).
Given,  Also, As we know that the sum of angles of a triangle is 180, so Now From (1) we have  Putting this value in (2) we have  Putting this in (3) And  Hence three angles of triangles
Let the speed of the train be v km/h and the time taken by train to travel the given distance be t hours and the distance to travel be d km.  Now As we Know, Now, According to the question,   Now, Using equation (1), we have  Also,   Adding equations (2) and (3), we obtain: Substituting the value of x in equation (2), we obtain: Putting this value in (1) we get, Hence...
Let the number of rows be x and number of students in a row be y. Total number of students in the class = Number of rows * Number of students in a row                                                             Now, According to the question,  Also,     Subtracting equation (2) from (1), we get: Substituting the value of y in equation (1), we obtain: Hence, The number of rows is 4...

Let the amount of money the first person and the second person having is x and y respectively

Noe, According to the question.

$x + 100 = 2(y - 100)$

$\Rightarrow x - 2y =-300...........(1)$

Also

$y + 10 = 6(x - 10)$

$\Rightarrow y - 6x =-70..........(2)$

Multiplying (2) by 2 we get,

$2y - 12x =-140..........(3)$

Now adding (1) and (3), we get

$-11x=-140-300$

$\Rightarrow 11x=440$

$\Rightarrow x=40$

Putting this value in (1)

$40-2y=-300$

$\Rightarrow 2y=340$

$\Rightarrow y=170$

Thus two friends had 40 Rs and 170 Rs respectively.

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Let the age of Ani be , age of Biju be , Case 1: when Ani is older than Biju age of Ani's father Dharam:    and age of his sister Cathy : Now According to the question, Also, Now subtracting (1)  from (2), we get, putting this in (1) Hence the age of Ani and Biju is 19 years and 16 years respectively. Case 2: And Now Adding (3) and (4), we get, putting it in (3) Hence the age of...
Let the speed of Ritu in still water be x and speed of current be y, Let's solve this problem by using relative motion concept, the relative speed when they are going in the same direction (downstream)= x +y  the relative speed when they are going in the opposite direction (upstream)= x - y Now, As we know, Relative distance = Relative speed * time . So, According to the question, And, Now,...
Given Equations, Let,  Now, our equation becomes And Now, Adding (1) and (2), we get Putting this value in (1) Now, And Now, Adding (3) and (4), we get Putting this value in (3), Hence,
Given Equations, Let,  Now, our equation becomes And By Cross Multiplication method, Now, And, Adding (3) and (4) we get, Putting this value in (3) we get, And Hence,
Given Equations, Let,  Now, our equation becomes And By Cross Multiplication method, And Hence,
Given Equations, Let,  Now, our equation becomes And By Cross Multiplication method, And Hence,
Given Equations, Let,  Now, our equation becomes And Multiplying (1) by 3 we get Now, adding (2) and (3) we get Putting this in (2) Now, Hence,
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