Question

Distance between Delhi and Jaipur is 300 km. Aman starts from Delhi and Rajiv from Jaipur at same time. After two hours, Aman realized he was travelling slow and therefore increased his speed by 25% and meet Rajiv at a point 108 km from Delhi. Find the increased speed of Aman, if Rajiv derived at a constant speed of 75 km/hr.

Answer 1

Answer:

55

Step-by-step explanation:

Answer 2

Given,

Distance between Delhi and Jaipur, $D=300km.$

Increase in Aman's speed, $25$% after $2hrs$.

Point of meeting, $108km$

Constant speed of Rajiv, $v_{R}=75km/h$

To find,

The increase in Aman's speed.

Solution,

Let the initial speed of Aman be $v_{A}$.

So, distance travelled by Aman in $2hrs$ will be,

$d_{A}=2v_{A}km$

Similarly,

Distance travelled by Rajiv in $2hrs$ will be,

$d_{R}=2v_{R}$

⇒$d_{R}=2$×$75$

⇒$d_{R}=150km$

And they both meet at a distance of $108km.$

So,

Distance traveled by Aman with speed increased by 25% will be

⇒$d'=(108-2v_{A})km$

And increased speed will be,
⇒$v_{i}=v_{A}.\frac{125}{100}$
⇒$v_{i}=\frac{5v_{A}}{4}km/h$

If Aman travelled $108km,$ Rajiv travelled $192km.$

So, they both are,

$(192-150)km = 42km$ away from each other.

Time taken by Rajiv to travel $42km$ will be,

⇒$\frac{42}{75} hrs$

⇒$\frac{14}{25}hrs$

This is equal to the time taken by Aman to travel $d'$ distance.

Hence,

⇒$\frac{d'}{v_{i}} =\frac{14}{25}$

⇒$\frac{108-2v_{A}}{\frac{5v_{A}}{4} } =\frac{14}{25}$

⇒$(108-2v_{A})(4)(25)=14(5v_{A})$

⇒$10800-200v_{A}=70v_{A}$

⇒$270v_{A}=10800$

⇒$v_{A}=\frac{10800}{270}$

⇒$v_{A}=40km/h$

Therefore,

Increase in speed of Aman is,

⇒$v_{i}=\frac{5v_{A}}{4}$

⇒$v_{i}=\frac{5(40)}{4}$

⇒$v_{i}=\frac{200}{4}$

⇒$v_{i}=50km/h$

Therefore, the increased speed of Aman is $50km/h$.