Question

divide 150 into 3 parts such that the second number is five -sixths the first and the third number is four - fifths the second.

Answer 1

ANSWER = 60 , 50 , 40

let the first number be x ,

$second \: number = \frac{5x}{6}$

$third \: number \: = \frac{4}{5} \times \frac{5x}{6}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{20x}{30}$

$x + \frac{5x}{6} + \frac{20x}{30} = 150$

$\frac{30x + 25x + 20x}{30} = 150$

$\frac{75x}{30} = 150$

$\frac{5x}{2} = 150$

$5x = 300$

$x = \frac{300 }{5}$

$x = 60$

FIRST NO. = 60

SECOND NO. = 50

THIRD NO. = 40

Answer 2

Answer

60, 50, & 40

Explanation :

Let's say first number gets $x$

Then, second number will get five-sixths of $x = \dfrac{5x}{6}$

And also, third number will get four-fifth of $\dfrac{5x}{6} = \dfrac{4x}{6}$

According to the question,

$\implies \: x + \dfrac{5x}{6} + \dfrac{4x}{6} = 150$

$\implies \: \dfrac{6x + 4x + 5x}{6} = 150$

$\implies \: \dfrac{15x}{6} = 150$

$\implies \: 15x = 150 \times 6$

$\implies \: x = \dfrac{150 \times 6}{15}$

$\therefore \: x = 60$

Hence,

First number gets = $x = 60$

Second number = $\dfrac{5x}{6} = 50$

Third number = $\dfrac{4x}{6} = 40$