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

Question 3 -

The students of a class are made to stand in rows .

If three students are extra in each row , there would be one row less .

If there are three less students in a row , there would be two rows more.

Find the number of students in the class .

Solution -

Let there be x students in the class and n number of rows .

Product of students and rows will always be equal -

=> xn

According to the first condition -

If three students are extra in each row , there would be one row less .

=> ( x + 3)( n - 1 )

So,

( x + 3)( n - 1 ) = xn

=> xn - x + 3n - 3 = xn

=> x - 3n = -3 ..... Equation 1

According to the second condition -

If there are three less students in a row , there would be two rows more.

=> ( x - 3)( n + 2 ) = xn

=> xn + 2x - 3n - 6 = xn

=> 2x - 3n = 6 ........ Equation 2

Subtracting the first equation from the second -

=> x = 9

So , the number of students is 9 .

Substituting this into any of the values -

=> n = 4

Thus , 4 rows can be formed.

This is the required answer .

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Question 4 -

A train covers a certain distance at a uniform speed. If the train had been 10 km faster , it would have taken 3 hours less than the scheduled time . the train had been 10 km slower , it would have taken 3 hours more than the scheduled time . Find the distance covered by the train .

Solution -

Let us assume that the train travels at a speed of x kmph and covers a distance d in a time t.

Speed = [ Distance / time ]

=> Distance = [ Speed ] × [ Time ]

=> d = ( x + 10 )( t - 3 )

=> d = xt - 3x + 10t - 30

=> 3x - 10t = -30 ...... { Equation 1 }

=> d = ( x - 10 )( t + 3 ).

=> d = xt + 3x - 10t - 30

=> 3x - 10t = 30 { Equation 2 }

But , this is not possible as Equation 1 and Equation 2 have three same variables on the LHS .

Thus , the answer is no solution

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Answer 2

Hello dear!

Here is your answer.

Kindly refer to the attachment.