A two digit number is such that the product of its digits us 8 ,if 18is added to the number the digits interchange. Their places.find the number
Answers
Let us consider,
One’s digit of a two digit number = x and Ten’s digit = y
The number is x + 10y
By interchanging the digits,
One’s digit = y and ten’s digit = x
The number is y + 10x
As per the statement, xy = 35 _____(1)
And, x + 10y + 18 = y + 10x
18 = y + 10x – x – 10y x – y = 2 _____(2)
using algebraic identity: (x + y)² = (x – y)² + 4xy (x + y)²
= (2)² + 4(35)² = 144 = 12 _____(3)
Subtracting (2) from (3), we get x = Form (1)
Answer: The number is x + 10y = 7 + 10(5) = 57
Answer:
Let the two numbers be x and y respectively.
xy = 8_(i)
10x + y + 18 = 10y + x
10x - x + 18 = 10y - y
9(x + 2) = 9y
x + 2 = y_(ii)
Putting the value y in equation.
(i) we get, x(x + 2) = 8
x² + 2x --8 = 0)
x² + 4x --2x --8 = 0
x(x + 4) - 2(x + 4) = 0
x - 2) (x + 4) = 0
x = 2 or 4
Putting the positive value of x in equation
(ii),2 + 2 = y = 4
Hence, The number is : 2 × 10 + 4 = 20 + 4 = 24