Question

a number is 42 more than average of its half,one third and one fifteenth find the no. . anwer = 60 formula please

Answer 1

hey
Let the number be x.

Half of a number will be x/2, and one-third of a number will be x/3, and one-fifteenth of a number will be x/15.

Average of half number + one-third + one-fifteenth = (x/2 + x/3 + x/15)/3

                                                                                      = (27/30)/3

                                                                                      = 3x/10.


Given that A number is 42 more than the average of x/2,x/3,x/15.

x - 42 = 3x/10

10x - 420 = 3x

-420 = 3x - 10x

-420 = -7x

x = 60.


Therefore the number = 60.


Hope this helps!

Answer 2

$\large {\green {\sf {\underline {\underline {Step-by-step \: Explanation}}}:-}}$

Let the number be x.

$Then, \: half \: of \: x = \frac{1}{2}x \\ \\ one-third \: of \: x = \frac{1}{3}x, \\ \\ one-fifteenth \: of \: x = \frac{1}{15}x$

Now, average of half, one-third and one-fifteenth of x

$= \frac{ (\frac{1}{2}x + \frac{1}{3}x + \frac{1}{15}x)} {3} \\ \\ = \frac{1}{3}( \frac{x}{2} + \frac{x}{3} + \frac{x}{15})$

$As \: per \: question, \: \: x = \frac{x}{6} + \frac{x}{9} + \frac{x}{45} + 42$

Transposing variables on one side and constant terms on other side, we get

$x - \frac{x}{6} - \frac{x}{9} - \frac{x}{45} = 42$

Multiplying both sides by 90, (the L.C.M. of 6, 9 and 15), we get

$90x - 15x - 10x - 2x = 42 \times 90 \\ \\ → 63x = 42 \times 90 \\ \\ x = \frac{42 \times 90}{63} = 60 \\ \\ Hence, \: the \: number \: is \: 60.$

$\large\color{blue}{I \: hope \: it \: helps \: you.}$

$\huge\dag\sf\red{By \: Divyanshu}$