Question

A number is divided into four parts such that 4 times the first part ,3times the second part, 6times to third part and 8 times the fourth part are all equal. In what ratio the number is divided??​

Answer 1

Step-by-step explanation:

i hope I have done it correctly....I mean all the calculations.

Answer 2

The number is divided in the ratio $6:8:4:3$

Step-by-step explanation:

Let the four parts of the number be m, n, o, and l.

Now, according to the question

Four times the first part $(4\times m)$

= Three times the second part $(3\times n)$

= Six times the third part $(6\times o)$

= Eight times the fourth part$(8\times l)$

= constant $(k)$

Thus, we can write m, n, o, and l in terms of k as

$4m = k$ ⇒ $m = \frac{k}{4}$

$3n = k$ ⇒$n = \frac{k}{3}$

$6o = k$    ⇒ $o = \frac{k}{6}$

$8l = k$    ⇒ $l = \frac{k}{8}$

Now, finding the ratios of all the four parts

$m:n:o:l = \frac{k}{4} : \frac{k}{3} : \frac{k}{6} : \frac{k}{8}$

Since k is common, it will get canceled from each term, and we will obtain the ratio as

$m:n:o:l = \frac{1}{4} : \frac{1}{3} : \frac{1}{6} : \frac{1}{8}$

Taking LCM and simplifying, we obtain

$m:n:o:l = \frac{6:8:4:3}{24}$

Removing 24 from the denominator

$m:n:o:l = 6:8:4:3$

Hence, the number is divided in the ratio $6:8:4:3$