Question

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class 10 ​

Answer 1

Question :

A two digit number is written in the form of an algebraic expression as shown 10x + y where x is digit at tens place and y is at unit place.

(a) The tens digit is three times the unit digit. The linear equation expressing the situation is

 Tens digit = x

 Units digit = y

⇒ x is 3 times y

x = 3y

x - 3y = 0

Hence, correct option is (iv)

(b) When number is decreased by 54, the digits are reversed. The new number formed is

If digits are reversed, the number obtained is 10y + x

  10x + y - 54 = 10y + x

  10x - x - 54 = 10y - y

  9x - 54 = 9y

  9(x - 6) = 9y

  x - 6 = y

  x - y - 6 = 0

Hence, correct option is (iii)

(c) Digit at tens place is

From (a) we get x = 3y

Substitute it in x - y - 6 = 0

 3y - y - 6 = 0

 2y - 6 = 0

   2y = 6

   y = 6/2

   y = 3 (unit digit)

Substitute in x = 3y, we get

x = 3(3) = 9

So, digit at tens place is 9

Hence, correct option is (i)

(d) Digit at unit place

 we got y = 3 [see solution (c)]

Unit digit = 3

Hence, correct option is (ii)

(e) Two digit number is

The number is 10x + y

Substitute the values of x and y,

The number = 10(9) + 3

The number = 90 + 3 = 93

Hence, correct option is (iv)