Question

the tail of fish is as long as its head plus 1/4th of its body.its body is three fourth of its whole length if its head is4cm long what is the total lengh of fish.

Answer 1

Total length of Fish is 128 cm.

Step-by-step explanation:

Let the total length of the fish be 'x'.

Given:

Head = 4 cm

body of fish is three fourth of its whole length.

framing in equation form we get;

Body = $\frac{3}{4}x$

Also Given:

the tail of fish is as long as its head plus 1/4th of its body.

framing in equation form we get;

Tail of fish = Head + $\frac{1}{4}$ Body.

Substituting the given value we get.

Tail of fish = $4+\frac{1}{4} \times \frac{3x}{4}=4+\frac{3}{16}x$

Now We know that;

Total Length of Fish  is equal Head plus Body plus Tail.

framing in equation form we get;

$x= 4+\frac{3}{4}x+4+\frac{3}{16}x\\\\x-\frac{3}{4}x-\frac{3}{16}x=8$

Using LCM for making Denominator common we get;

$\frac{16x}{16}-\frac{3x\times4}{4\times4}-\frac{3x\times1}{16\times16}=8\\\\\frac{16x}{16}-\frac{12x}{16}-\frac{3x}{16}=8\\\\\frac{16x-12x-3x}{16}=8\\\\16x-12x-3x = 8 \times 16\\\\x= 128\ cm$

Hence Total length of Fish is 128 cm.