Advertisements
Advertisements
प्रश्न
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
Advertisements
उत्तर
Let the two digits be:
Tens digits be x and units = 16/x
Number `=10x+16/x`
Number obtained by interchanging `=10xx16/x+x`
`rArr(10x+16/x)-(10xx16/x+x)=54`
`rArr10x+16/7-160/x+x=54`
⇒ 10x2 + 16 - 160 - x2 = 54x
⇒ 9x2 - 54x - 144 = 0
⇒ x2 - 6x - 16 = 0
⇒ x2 - 8x + 2x - 16 = 0
⇒ x(x - 8) + 2(x - 8) = 0
⇒ (x - 8)(x + 2) = 0
⇒ x - 8 = 0
⇒ x = 8
Or
⇒ x + 2 = 0
⇒ x = -2
But, a digit can never be negative, hence x = 8
Hence the required number `=10x+16/x=10(8)+16/8=80+2=82`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0
Solve the following quadratic equations by factorization:
`x^2-(sqrt3+1)x+sqrt3=0`
Solve the following quadratic equations by factorization:
3x2 − 14x − 5 = 0
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
The sum of natural number and its positive square root is 132. Find the number.
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
Find the values of p for which the quadratic equation
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
Solve the following equation: 4x2 + 16x = 0
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + 6x + 5 = 0; x = -1, x = -5
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
