Advertisements
Advertisements
Question
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
Advertisements
Solution
Let a digit at unit's place be x and at ten's place by y.
then according to problem
Required no.
= 10y + x
On interchanging the digits
Number formed
= 10 x + y
xy = 12
∴ x = `(12)/y`
10y + x + 36 = 10x + y
10y + x - 10x - y = -36
9y - 9x = -36
9(y - x) = -36
y - x = `-(36)/(9)`
y - x = -4
On substituting value of x = `(12)/y`
`y - (12)/y` = -4
`(y^2 - 12)/y` = -4
y2 + 4y - 12 = 0
y2 + 6y - 2y - 12 = 0
y (y + 6) -2 (y + 6) = 0
(y + 6) (y - 2) = 0
y = -6, 2
When y = 2
x = `(12)/(2)` = 6
Required no.
= 10y + x
= 10 x 2 + 6
= 20 + 6
= 26.
RELATED QUESTIONS
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve each of the following equations by factorization :
`6/x=1+x`
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
If y = 1 is a common root of the equations \[a y^2 + ay + 3 = 0 \text { and } y^2 + y + b = 0\], then ab equals
Solve the following equation: 4x2 + 16x = 0
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
