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.
Solution
Let 2-digit number = xy = 10x + y
Reversed digits = yx = 10y + x
According to question,
xy = 6
y = `(6)/x` ...(i)
and
10x + y + 9 = 10y + x
⇒ `10x + (6)/x + 9 = 10 xx (6)/x + x ...("From" (i) y = (6)/x)`
⇒ 10x2 + 6 + 9x = 60 + x2
⇒ 10x2 - x2 + 9x + 6 - 60 = 0
⇒ 9x2 + 9x - 54 = 0
⇒ x2 + x - 6 = 0
⇒ x2 + 3x - 2x - 6 = 0
⇒ x(x + 3) -2(x + 3) = 0
⇒ x = 2 or -3 ...(rejacting -3)
putting the value of x in (i)
y = `(6)/(2)` = 3
∴ 2-digit
= 10x + y
= 10 x 2 + 3
= 23.
APPEARS IN
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.
Solve:
`1/(x + 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
Solve the following quadratic equations by factorization: \[\frac{1}{2a + b + 2x} = \frac{1}{2a} + \frac{1}{b} + \frac{1}{2x}\]
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
Find the values of x if p + 1 =0 and x2 + px – 6 = 0
Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
