Question

Maths
Class 10
Chapter - 3
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•Please answer the given 2 questions,answer all the questions.
•Please don't spam otherwise I will spam on your questions...LOL.
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Thanks
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Answer 1

Answer:

Step-by-step explanation:

Let the speed of car starting from A be 'x' km/h and speed of car starting from B be 'y' km/h.

Total distance=80 km

Also 1 hour 20 mins= 4/3 hour

As per given condition, When car moves in same direction,

Distance travelled by y= 8y km

Distance travelled by x= 8x= 80+8y

Now, Equation formed is 8x=80+8y

=> 8x-8y=80

=> x-y=10 ----(1)

Similarly, For opposite direction,

Distance travelled by x= (4/3)x

Distance travelled by y= (4/3) y

Also total distance covered= 4/3*x+4/3y

=> 80= 4x+4y/3

=> 240= 4x+4y

=> 60=x+y ----(2)

Solving Equation (1) and (2)

60=x+y ----(2)

x-y=10 ----(1)

=> x= 10+y ----(3)

Substituting the value of (3) in (2) we get,

60= 10+y+y

=> 60-10=2y

=> 50=2y

=> 25=y

Also, x=10+y=> x= 10+25=> x=35

Therefore Speed of car starting from A is 35km/h

Speed of car starting from B is 25km/h

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Answer 2

Question 1 -

The sum of a two digit number and the number obtained by reversing it's digits is 66.

If the digits of the number differ by 2, find the number .

How many such numbers are there ?

Solution -

First of all , in these types of questions , there are always two such numbers namely the number and it's reciprocal .

Now , let us assume that the number is xy .

Sum of the digits of the number - => 10x + y

Reversed number - yx

Sum of the digits of the number - =>10y + x

Sum - => 10x + y + 10y + x => 11 ( x + y )

But , this is equal to 66 .

So, 11 ( x + y ) = 66=>x + y = 6 . . . . { Equation 1 }

Now , digits of the number differ by 2 .

So , x - y = 2 . . . { Equation 2 }

Adding these two equations -

=> 2x = 8

=> x = 4

=> y = 2 .

Thus , the required number is 42 or 24 .

This is the answer . ________________________________________________________

Question 2 -

Places A and B are 80 km apart from each other on a highway .

A car starts from A and another from B at the same time .

If they move in the same direction , they meet in 8 hrs and if they move In the opposite directions , they meet in 1 hour 20 minuites.

Find the speed of both cars.

Solution -

Let us assume that the two cars A and B moves with the speeds x and y respectively .

If they move In the same direction

- Net speed becomes - => ( x - y ) .

But, speed = [ Distance Travelled ] / [ Time taken ]

= [ 80 / 8 ] = 10 kmph

So , [ x - y ] = 10. ....... { Equation 1 }

If they move in opposite directions -

Net speed becomes - ( x + y )

But, speed = [ Distance Travelled ] / [ Time taken ]

= [ 80 / (4 / 3 ) ] = 60 kmph

. => ( x + y ) = 60 ......... { Equation 2 }

Adding the two equations :

=> x = 35 kmph

=> y = 25 kmph .

This is the required answer .

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