Advertisements
Advertisements
Question
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Advertisements
Solution
Let the unit's digit be x then tens digit will be `(6)/x`, then two digit number is `(60)/x + x.`
From question,
`(60)/x + x + 9 = 10x + (6)/x`
60 + x2 + 9x = 10x2 + 6
9x2 - 9x - 54 = 0
x2 - x - 6 = 0
x2 - 3x + 2x - 6 = 0
x (x - 3) + 2 (x - 3) = 0
(x - 3) (x +2) = 0
⇒ x = -2 or 3
As x can't be-ve
So, required two digit number
= `(60)/(3) + 3`
= 23.
RELATED QUESTIONS
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Solve : x2 – 11x – 12 =0; when x ∈ N
One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
Solve the following equation by factorization
3x2 – 5x – 12 = 0
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
