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ques no 12 of rs Agrawal class 10 ch 3 linear equation
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Answer 1

Answer:

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Step-by-step explanation:

let the required two digit number be 10x+y

wherein digit at tens place is x and that of units place is y

so thus number obtained by reversing digits is

10y+x

so according to first condition

10x+y=7(x+y)

ie 10x+y=7x+7y

so 3x=6y

ie x=2y (1)

according to the second condition

10x+y-27=10y+x

so ie 9x-9y=27

ie x-y=3 (2)

substitute value of x from (1) in (2)

we get

y=3

substitute value of y in any of two equations

we get

x=6

so our assumed two digit number=10x+y

=(10×6)+3

=60+3

=63

thus our required two digit number is 63

Answer 2

Let the :

• Units place digit be x
• Tens place digit be 10y
• Number will be 10y + x

According to the question :

• A number consisting of two digits = 7 (Sum of its digits)
• (10y + x) = 7 (x + y)
• 10y + x = 7x + 7y
• 10y - 7y = 7x - x
• 3y = 6x
• 3y - 6x = 0 . . . . . . (1)

Also, given that :

• Original number - 27 = Digits are reversed
• (10y + x) - 27 = (10x + y)
• 10y + x - 27 - 10x - y = 0
• 9y - 9x = 27
• Divide the whole equation be 9.
• y - x = 3 . . . . . . . . (2)

Getting the value of y from (1) :

• 3y - 6x = 0
• 3y = 6x
• y = 6x/3
• y = 2x . . . . . . . (3)

Substituting the value of y from (3) in (2) :

• y - x = 3
• 2x - x = 3
• x = 3

Niw, substituting x value in (3) to get y :

• y = 2x
• y = 2 (3)
• y = 6

So, the values are :

• Units place digit : x = 3
• Tens place digit : y = 6

The required number is :

• 10y + x
• 10 (6) + 3
• 60 + 3
• 63

Therefore, the number is 63.