Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
Solve the following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x
Find two numbers whose sum is 27 and product is 182.
Find the consecutive numbers whose squares have the sum 85.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?
Solve the following equation by factorisation :
`sqrt(3x^2 - 2x - 1) = 2x - 2`
