15. A two digits number is 5 times the sum of its digits and this numb

1.	15. A two digits number is 5 times the sum of its digits and this number is also equal to 5more than twice the product of its digits. Find the two digits number.
Answer» 10 is the 2 digit number Let the digits of two digit are x and y Then number = 10x + y As per given condition 10x + y = 5(x + y)10x - 5x = 5y - y5x = 4yx = 4y/5........... (1) 10x + y = 2xy + 5 Put value of x from eq(1) 24y + y = 24y^2 /5 + 59y = 8y^2/5 + 58y^2 + 25 - 45y = 08y^2 - 40y - 5y + 25 = 08y(y - 5) - 5(y - 5) = 0(8y - 5)(y - 5) = 0y = 5/8, 5 As digits are only integer so, value of y = 5 From eq(1)x = 45/5 = 4 Therefore, Number = 410 + 5 = 45

15. A two digits number is 5 times the sum of its digits and this number is also equal to 5more than twice the product of its digits. Find the two digits number.

Answer»

10 is the 2 digit number

Let the digits of two digit are x and y

Then number = 10x + y

As per given condition 10x + y = 5(x + y)10x - 5x = 5y - y5x = 4yx = 4y/5........... (1)

10x + y = 2xy + 5 Put value of x from eq(1)

2*4y + y = 2*4y^2 /5 + 59y = 8y^2/5 + 58y^2 + 25 - 45y = 08y^2 - 40y - 5y + 25 = 08y(y - 5) - 5(y - 5) = 0(8y - 5)(y - 5) = 0y = 5/8, 5

As digits are only integer so, value of y = 5

From eq(1)x = 4*5/5 = 4

Therefore, Number = 4*10 + 5 = 45