Q1

Find the area of a rectangle whose length and breadth are (x+y) and (x * - xy + y*) respectively.

Q 2

Sum of the digits of a two-digit number is 9. When we

interchange the digits, it is found that the resulting new

number is greater than the original number by 27. What is the two-digit number?

36

Step-by-step explanation:

1

Assuming x = x * and y = y*

(x+y) (x * - xy + y*) = x² - x²y + xy + xy - xy² + y² = x² - x²y + 2xy - xy² + y²

Assuming x! = x * and y! = y*

(x+y) (x * - xy + y*) = xx * - x²y + xy * + x*y - xy² + yy*

2

Sum of the digits of a two-digit number is 9.

Two digits number = xy

x + y = 9

When we interchange the digits, it is found that the resulting new

number is greater than the original number by 27.

yx = xy + 27

First find all the pairs of numbers that sum to make 9

0 + 9

1 + 8

2 + 7

3 + 6

4 + 5

Find the difference between the digits in the form xy and yx.

90 - 09 = 81

81 - 18 = 63

72 - 27 = 47

63 - 36 = 27

54 - 45 = 9