Arun Sharma Solutions for Exercise 2: Level of Difficulty

Ayrton Senna had to cover a distance of $60 \mathrm{km}$60 km. However, he started $6$minutes later than his sched uled time and raced at a speed $1 \mathrm{km}/\mathrm{h}$ higher than his originally planned speed and reached the finish at the time he would reach it if he began to race strictly at the appointed time and raced with the assumed speed. Find the speed at which he travelled during the journey described.

An urgent message had to be delivered from the house of the Peshwas in Pune to Shivaji who was camping in Bangalore. A horse rider travels on horse back from Pune to Bangalore at a constant speed. If the horse in creased its speed by $6 \mathrm{km}/\mathrm{h}$, it would take the rider $4 \mathrm{hours}$ less to cover that distance. And travelling with a speed $6 \mathrm{km}/\mathrm{h}$ lower than the initial speed, it would take him $10 \mathrm{hours}$more than the time he would have taken had he travelled at a speed $6 \mathrm{kmph}$kmph higher than the initial speed. Find the distance between Pune and Bangalore

Three brothers, Ram, Shyam and Mohan, travelled by road. They all left the college at the same time-12 noon. The description of the motions of the three are detailed below:

Three brothers, Ram, Shyam and Mohan, travelled by road. They all left the college at the same time-12 noon. The description of the motions of the three are detailed below:

In the above question, who reached last and at what time?

A motorcyclist rode the first half of his way at a constant speed. Then he was delayed for $5 \mathrm{minutes}$and, therefore, to make up for the lost time he increased his speed by $10 \mathrm{km}/\mathrm{h}$. Find the initial speed of the motorcyclist if the total path covered by him is equal to $50 \mathrm{km}$.

Ram Singh and Priyadarshan start together from the same point on a circular path and walk around, each at his own pace, until both arrive together at the starting point. If Ram Singh performs the circuit in $3 \mathrm{minutes} 44 \mathrm{seconds}$ and Priyadarshan in $6 \mathrm{minutes} 4 \mathrm{seconds},$ how many times does Ram Singh go around the path?

Ravi, who lives in the countryside, caught a train for home earlier than usual yesterday. His wife normally drives to the station to meet him. But yesterday he set out on foot from the station to meet his wife on the way. He reached home $12 \mathrm{minutes}$ earlier than he would have done had he waited at the station for his wife. The car at a uniform speed, which travels at a is $5$times Ravi’s speed on foot. Ravi reached home at exactly $6$O’clock. At what time would he have. Reached home if his wife, forewarned of his plan, had met him at the station?

Hemant and Ajay start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lane and at uniform speeds, but Hemant is faster than Ajay. They first pass at a point $18.5 \mathrm{m}$ from the deep end and having completed one. Length, each one is allowed to rest on the edge for exactly $45 \mathrm{seconds}$. After setting off on the return length, the swimmers pass for the second time just $10.5 \mathrm{m}$ from the shallow end. How long is the pool?