CoCubes Number, Relations and Functions Question and Answers Quiz-1

Explanation:

Let the ten's digit be x and unit's digit be y.

Then, (10x + y) - (10y + x) = 36

 9(x - y) = 36

 x - y = 4.

let unit,s digit be y and tens digit be x ,then

xy=8 ————-(1)

yx=xy+18 ———(2)

from equation 2 by simplifying it ,we get:-

10y+x=10x +y +18

9y=9x+18 ,then divide both side of the equation by 9

y=x+2 ————-(3)

from equations 1 and 3 by substituting y by x+2 ,we get:-

xy=8 , x(x+2) =8

x²+2x=8 , x²+2x-8=0

then we solve the quadratic equation for what method that is easy for you either by completing square ,factoring method or by formula

now I am using by factoring

x²+2x-8=0

=>x²+4x-2x-8=0

=>x(x+4)-2(x+4) =0

=>(x+4)(x-2) =0

x+4=0 ,x-2=0

x=-4 , x=2

we omitted negative number and took positive integer that is x=2

then, y=x+2 =2+2=4

the number is the form of (xy) =10x+y=24

Therefore the number is 24

Let the numbers be a, b and c.

Then, a² + b² + c² = 138 and (ab + bc + ca) = 131.

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

 (a + b + c) = √400 = 20.

Let the ten's digit be x and unit's digit be y.

Then, x + y = 15 and x - y = 3   or   y - x = 3.

Solving x + y = 15   and   x - y = 3, we get: x = 9, y = 6.

Solving x + y = 15   and   y - x = 3, we get: x = 6, y = 9.

So, the number is either 96 or 69.

Hence, the number cannot be determined.

Let the ten's digit be x.

Then, unit's digit = x + 2.

Number = 10x + (x + 2) = 11x + 2.

Sum of digits = x + (x + 2) = 2x + 2.

 (11x + 2)(2x + 2) = 144

 22x² + 26x - 140 = 0

 11x² + 13x - 70 = 0

 (x - 2)(11x + 35) = 0

 x = 2.

Hence, required number = 11x + 2 = 24.

Explaination:

Let the number be x

Then x + 17 = 60/x

x² + 17x - 60 = 0

(x  + 20) (x - 3) = 0

x = 3

Let the number be x and y

Then,  xy= 9375 and x/y = 15

(xy)/(x/y) = 9375/15

y² = 625

y = 25

x = 15y = (15 * 25) = 375

sum of numbers = x + y

=375 + 25 = 400

Let the numbers be x and y.

Then, xy = 120 and x² + y² = 289.

(x + y)² = x ²+ y² + 2xy = 289 + (2 x 120) = 529

x + y = √529 = 23.

Explanation:

Let the numbers be x and x + 2.

Then, (x + 2)² - x² = 84

4x + 4 = 84

4x = 80

x = 20.

The required sum = x + (x + 2) = 2x + 2 = 42.

Let the number be x.
then 1/3 of 1/4 of x = 15
=> x = 15*3*4
=> 180

So, the required no. is (3/10) * 180 = 54