Question

a man travelled three forth of his journey by train, one fifth by bus and the remaining 6 km by auto. what is the length of his journey

Answer 1

Let the total journey be X

therefore journey by train = 3/4 *x

journey by bus = 1/5 *x

therefore ,
3X/4 + X/5 + 6 = X

19X/20 + 6 = X

X - 19X/20 = 6

X/20 = 6

X = 120 km

Answer 2

Let the total length of his journey be x

So,
Journey covered by train =
$\frac{3}{4} x$

Journey covered by Bus =
$\frac{1}{5} x$

Journey covered by Auto =
$6km$

Now, adding all three equation, we will get the total distance covered

$\frac{3}{4} x + \frac{1}{5} x + 6 = x$
$\frac{3}{4} x + \frac{1}{5} x - x = - 6$

Taking L.C.M. = 20 in L.H.S.

$\frac{15x + 4x - 20x}{20} = - 6$

$\frac{19x - 20x}{20} = - 6$

$\frac{ - x}{20} = - 6$

$- x = - 6 \times 20$

$- x = - 120$

$x = 120$

Hence, the value of x is 120 km, i.e. the total length of the man's journey was 120 km.

That is your answer.

VERIFICATION

Assigning the value of x in equation number 4, we get

$\frac{3}{4} x + \frac{1}{5} x + 6 = x$

$( \frac{3}{4} \times 120) + ( \frac{1}{5} \times 120) + 6 = 120$

$( \frac{360}{4} ) + ( \frac{120}{5} ) + 6 = 120$

$90 + 24 + 6 = 120$

$90 + 30 = 120$
$120 = 120$


Therefore, L.H.S. = R.H.S.
Hence, the value of x = 120 is correct

Hope it'll help.