Question

Raj while going by bus from home to
airport (without any halt) takes 20 min
less than time taken when the bus halts
for some time. The average speed is
8 km/h more than the average speed of
the bus when it halts. If the distance
from home to airport is 60 km, what is
the speed of the bus when it is travelled?
[IBPS Clerk (Mains) 2017]
(a) 24 km/h (b) 46 km/h
(c) 20 km/h (d) 49 km/h
(e) 42 km/h​

Answer 1

Answer:

(e) 42 km/h

Step-by-step explanation:

Let us assume that the bus speed is x Km/hr.

Given the distance from home to the airport is 60 Km.

So, time taken to cover this distance without any halt is $\frac{60}{x}$ hours.

Again given that, 20 minutes(or, $\frac{1}{3} hours$) more time is required to cover this distance when halts are taken.

So, time taken to cover this distance with halt is $(\frac{60}{x}+\frac{1}{3})$ hours.

Now, it is also given that the difference of average speed between with and without halts journey is 8 Km/hour.

The average speed is given by the following formula

Average speed= (Total distance traveled / Total time taken to travel)

So, for the above condition, the equation can be written as

$\frac{60}{\frac{60}{x}}-\frac{60}{(\frac{60}{x}+\frac{1}{3})}=8$

⇒ $x-\frac{60(3x)}{180+x}=8$

⇒ $180x+x^{2} -180x=8(180+x)$

⇒ $x^{2} -8x-1440=0$

⇒ $x=\frac{8+\sqrt{64+4*1440} }{2}$  {Ignoring the negative root as x can not be negative}

⇒ x= 42.15 Km/hour = 42 Km/hour (Approximate)

(Answer)

Answer 2

Answer:

(e) 42 km/h

Step-by-step explanation:

Let us assume that the bus speed is x Km/hr.

Given the distance from home to the airport is 60 Km.

So, time taken to cover this distance without any halt is \frac{60}{x}

x

60

hours.

Again given that, 20 minutes(or, \frac{1}{3} hours

3

1

hours ) more time is required to cover this distance when halts are taken.

So, time taken to cover this distance with halt is (\frac{60}{x}+\frac{1}{3})(

x

60

+

3

1

) hours.

Now, it is also given that the difference of average speed between with and without halts journey is 8 Km/hour.

The average speed is given by the following formula

Average speed= (Total distance traveled / Total time taken to travel)

So, for the above condition, the equation can be written as

\frac{60}{\frac{60}{x}}-\frac{60}{(\frac{60}{x}+\frac{1}{3})}=8

x

60

60

−

(

x

60

+

3

1

)

60

=8

⇒ x-\frac{60(3x)}{180+x}=8x−

180+x

60(3x)

=8

⇒ 180x+x^{2} -180x=8(180+x)180x+x

2

−180x=8(180+x)

⇒ x^{2} -8x-1440=0x

2

−8x−1440=0

⇒ x=\frac{8+\sqrt{64+4*1440} }{2}x=

2

8+

64+4∗1440

{Ignoring the negative root as x can not be negative}

⇒ x= 42.15 Km/hour = 42 Km/hour (Approximate)

(Answer)

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