Question

i have been travelling from place A to place B.On the first day i travelled one-quarter of the distance On the second day, I travelled one-half of the remaining distance On the third day, I travelled three-quarters of the remaining distance. Yesterday, I travelled one-third of the remaining distance. I now have 21 km left to travel. What is the total distance between the places?

Answer 1

it is 336 km l am sure because the answer is given on the back of my book

Answer 2

Answer:

The total distance between the places A and B is 336 km.

Step-by-step explanation:

Let total distance travelled from place A to Place B be $x$.

Distance travelled on first day = $\frac{1}{4}$ of the distance

                                                   = $\frac{1}{4} \cdot x$

                                                   = $\frac{x}{4}$

Remaining distance = $x-\frac{x}{4}$

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

Distance travelled on second day = $\frac{1}{2}$ of the remaining

                                                         = $\frac{1}{2} \cdot \frac{3x}{4}$

                                                         = $\frac{3x}{8}$

Remaining distance = $x-\frac{x}{4}-\frac{3x}{8}$

                                 = $\frac{3x}{8}$

Distance travelled on third day = $\frac{3}{4}$ of the remaining

                                                    = $\frac{3}{4} \cdot \frac{3x}{8}$

                                                    = $\frac{9x}{32}$

Remaining distance = $x-\frac{x}{4}-\frac{3x}{8}-\frac{9x}{32}$

                                 = $\frac{3x}{32}$

Distance travelled on yesterday = $\frac{1}{3}$ of the remaining

                                                      = $\frac{1}{3}\cdot \frac{3x}{32}$

                                                      = $\frac{x}{32}$

Distance left to reach at place B = 21 km

Now,

Total distance, $x$ = $\frac{x}{4}+\frac{3x}{8} +\frac{9x}{32}+\frac{x}{32}+21$

⇒ $x=\frac{8x+12x+9x+x}{32} +21$

⇒ $x=\frac{30x}{32} +21$

⇒ $x-\frac{30x}{32} =21$

⇒ $\frac{32x-30x}{32} =21$

⇒ 2$x$ = 21 × 32

⇒ $x$ = 21 × 16

⇒ $x$ = 336

Therefore, the total distance between the places A and B is 336 km.

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