Question

a man cover 2/5 of his journey by taxi , 1/4 of his journey by auto and the remaining 14 km by bus. what is the length of his total journey?​

Answer 1

• Let the length of his total journey be (M) km.

》 A man covers 2/5 of his journey by taxi, 1/4 of his journey by auto.

=> $\dfrac{2}{5}$ of total journey + $\dfrac{1}{4}$ of total journey.

=> $\dfrac{2M}{5}$ + $\dfrac{1M}{4}$

=> $\dfrac{8M\:+\:5M}{20}$

=> $\dfrac{13M}{20}$

》 The remaining journey of man is 14 km by bus.

=> Total journey - Remaining journey

=> M - 14

According to question,

=> M - 14 = $\dfrac{13M}{20}$

Cross multiply them

=> 20(M - 14) = 13M

=> 20M - 280 = 13M

=> 20M - 13M = 280

=> 7M = 280

=> M = 40

_____________________________

Total length of his journey is 40 km.

_____________ [ ANSWER ]

_____________________________

☆ VERIFICATION :

From above calculations we have M = 40

Put value of M in this : M - 14 = $\dfrac{2M}{5}$ + $\dfrac{1M}{4}$

=> M - 14 = $\dfrac{13M}{20}$

=> 40 - 14 = $\dfrac{13(40)}{20}$

=> 26 = $\dfrac{520}{20}$

=> 26 = 26

______________________________

Answer 2

SOLUTION

Let his total journey length be x.

Therefore,

Then, distance travelled by taxi

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

Travelled by auto=

$\frac{1}{4} x$

Therefore,

Total journey travelled by taxi & auto

$= > \frac{2}{5} x + \frac{1}{4} x \\ \\ = > \frac{8x + 5x}{20} \\ \\ = > \frac{13}{20} x$

So, Remaining journey

$= > x - \frac{13}{20} x = \frac{20x - 13x}{20} \\ \\ = > \frac{7}{20} x$

According to the question, remaining journey is 14km by Bus.

$= > \frac{7x}{20} = 14 \\ = > 7x = 14 \times 20 \\ = > x = \frac{14 \times 20}{7} \ \\ = > x = 2 \times 20 \\ = > x = 40km$

Hence, the length of his journey= 40km.

Hope it helps ☺️