31. A scooterist covers a certain distance at 36 km/hr. How much distance does he cover in 3 min?
a. 1500 m
b. 1600 m
c. 1800 m
d. 2400 m

Answer: C

Explanation:
Speed = 36 km/hr = 36 × $\displaystyle\frac{5}{{18}}$ × m/s = 10 m/s
Thus, the distance covered in 3 min = (10 × 3 × 60) = 1,800 m.

32. The ratio between the rates of walking of P and Q is 2 : 3. If the time taken by Q to cover a certain distance is 36 minutes, the time taken by P to cover that much distance is :
a. 24 min
b. 54 min
c. 48 min
d. 21.6 min

Answer: B

Explanation:
Ratio of times taken = $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}$ = $3 : 2$
Let $P$ takes $x$ minutes to cover the distance.
$ \Rightarrow \dfrac{3}{2} = \dfrac{x}{{36}}$
$ \Rightarrow$ x = 54 minutes.

33. A man, on tour, travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. the average speed for the first 320 km of the tour, is :
a. 35.55 km/hr
b. 71.11 km/hr
c. 36 km/hr
d. 72 km/hr

34. A man travels 35 km partly at 4 km/hr and at 5 km/hr. If he covers former distance at 5 km/hr and later distance at 4 km/hr, he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is
a. 9 hours
b. 7 hours
c. $4\displaystyle\frac{1}{2}$ hours
d. 8 hours

Answer: D

Explanation:
Suppose the man covers first distance in x hrs.and second distance in y hrs. Then,
$4x + 5y = 35$ and $5x + 4y = 37$
Solving the equations,
we get $x$ = 5 and $y$ = 3
Total time taken = (5 + 3)hrs = 8 hrs

35. Rama travels a certain distance at 3 km/hr and reaches 15 min.late. If he travels at 4 km/hr he reaches 15 min.earlier. The distance he has to travel is :
a. 4.5 km
b. 6 km
c. 7.2 km
d. 12 km

Answer: B

Explanation:
Let the distance be x km.
Then, $\displaystyle\frac{x}{3} - \displaystyle\frac{x}{4} = \displaystyle\frac{{30}}{{60}}$ or $\displaystyle\frac{{4x - 3x}}{{12}}$
or $\displaystyle\frac{{4x - 3x}}{{12}} = \displaystyle\frac{1}{2}$ or x = 6 km.

36. Raghuveer has to cover a distance of 6 km in 45 minutes. If he covers one half of the distance in $\displaystyle\frac{2}{3}$rd time, what should be his speed to cover the remaining distance in the remaining time ?
a. 12 km/hr
b. 16 km/hr
c. 3 km/hr
d. 8 km/hr

Answer: A

Explanation:
Time left = $\left( {\displaystyle\frac{1}{3} \times \displaystyle\frac{{45}}{{60}}} \right)$ hr = $\displaystyle\frac{1}{4}$ hr
Distance left = 3 km
Speed required = $\left( {3 + \displaystyle\frac{1}{4}} \right)$ km/hr = 12 kmph