Question

35. Two cars start at the same time from A and B towards each other the speed of car 30 kmph and 50 kmph.
. By the time two cars meet, one car had covered 160 km more than the other.
What is the distance between A and B?
(a) 560 km
(b) 520 km (C) 600 km (d) 640 km (e) None of these
​

Answer 1

D/30=160+D/50

5D=3D+480

D=240.

Total distance is D+(160+D)

= 640Km

Answer 2

The distance between A and B is 640 km. Thus Option D is correct

Solution:

Let us assume distance traveled by car moving with 30 kmph is "d", then the distance traveled by car moving with 50 kmph is (d+160)

The formula for speed distance time is given as:

$\text { Speed }=\frac{\text { Distance }}{\text { Time }}$

$time = \frac{distance}{speed}$

The time taken by car moving with 30 kmph with distance "d" is given as:

$\text {time}=\frac{d}{30}$ --- eqn 1

The time taken by car moving with 50 kmph with distance "d + 160" is given as:

$time=\frac{d+160}{50}$ --- eqn 2

When the both cars meet, eqn 1 = eqn 2

$\begin{array}{l}{\frac{d}{30}=\frac{d+160}{50}} \\\\ {\text { On solving }} \\\\ {50 \mathrm{d}=30(\mathrm{d}+160)} \\\\ {50 \mathrm{d}=30 \mathrm{d}+4800} \\\\ {20 \mathrm{d}=4800} \\\\ {\mathrm{d}=4800 \div 20=240}\end{array}$

Which is the distance travelled by the car moving with 30kmph

Distance traveled by car moving with 50 kmph = d + 160 = 240 + 160 = 400 km

Total distance =  distance travelled by the car moving with 30kmph + Distance traveled by car moving with 50 kmph

Total distance between A and B = 240 + 400 = 640 km

Thus Option D is correct

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