Advertisements
Advertisements
Question
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Advertisements
Solution
Let the tens digit be x
Then, the units digit = 12/x
`therefore " Number" =10x+12/x`
And, number obtained by interchanging the Digits `= 10xx12/x+x=120/x+x`
`rArr10x+12/x+36=120/x+x`
`rArr9x+(12-120)/x+36=0`
⇒ 9x2 - 108 + 36x = 0
⇒ 9(x2 + 4x - 12) = 0
⇒ x2 + 6x - 2x - 12 = 0
⇒ x(x + 6) - 2(x + 6) = 0
⇒ (x - 2)(x + 6) = 0
∴ x = 2 or x = -6
But, a digit can never be negative, x = 2
Hence, the digit `=10x+12/x=10(2)+12/2=20+6=26`
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
2x2 + x – 6 = 0
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.
Solve the following quadratic equations by factorization:
x2 + 2ab = (2a + b)x
Solve the following quadratic equations by factorization:
`x^2 – (a + b) x + ab = 0`
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Write the sum of real roots of the equation x2 + |x| − 6 = 0.
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =
Solve the following equation: 2x2 - 3x - 9=0
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve the following equation: `7"x" + 3/"x" = 35 3/5`
Solve the following equation : x2 + 2ab = (2a + b)x
Solve the following equation: abx2 +(b2-ac) x - bc = 0
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve equation using factorisation method:
x2 – 10x – 24 = 0
Solve the following equation by factorization
3(x – 2)2 = 147
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
