**1.A car completes a journey in 10 hours, if it covers half of the journey at 40 km/hr and the remaining at 60 km/hr. The distance covered by car is:**

(a) 400 km

**(b) 480 km**

(c) 380 km

(d) 300 km

(e) None of the above

**Let the total distance covered by car = 2d**

**According to question total time = 10hr**

**d/40+d/60=10**

**5d/120=10**

**d = 240**

**2d = 480 km**

**2.A bus meets with an auto at 10:00 am while going the same way in the same direction towards Haridwar. The Bus reach at Haridwar at 12:30 p.m. and take 1 hour rest at there. Bus return on the same way and meet with the same auto half an hour later. At what time the auto will reach at Haridwar?**

**(a) 3 pm**

(b) 4 pm

(c) 3:30 pm

(d) 5 pm

(e) None of the above

**Let C is point where the auto and the bus meet first time and D is a point where the auto and the**

**Bus meet 2nd time.**

**According to the above diagram:**

**Distance C D covered by Bus in 2 hour and auto covered the same distance in 4 hr.**

**Distance C B covered by Bus 2.5 hr**

**And by Auto in double of Bus = 2.5 × 2 = 5 hour**

**Time = 10 + 5 = 3 pm**

**3.In covering a distance of 30 km, Arun takes 2 hours more than Sumit. If Arun doubles his speed, then he would take 1 hour less than Sumit. Arun’s speed in (km/hr) is:**

**(a) 5**

(b) 6.25

(c) 6

(d) 7.5

(e) None of the above

**Let the Arun speed is x km/hr and**

**Sumit speed is y km/hr**

**30/x¬-30/y=2 …(i)**

**30/y-30/2x=1 …(ii)**

**On adding (i) and (ii)**

**30/x-30/2x=3**

**(60-30)/2x=3**

**30/2x=3**

**x = 5 km/hr**

**4. A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his initial speed per hour.**

(a) 6 km/hr

(b) 5 1/2 km/hr

(c) 4 km/hr

**(d) 5 km/hr**

(e) None of the above

**This speed after reduction =1-1/15=14/15**

**His time change =15/14**

**New time = 15t**

**Old time = 14t**

**14t = 30**

**t = 30/14**

**15t =30/14×15**

**He travels 10 km less in time =450/14-30**

**=(450-420)/14=30/14**

**His new speed = 10/30×14=14/3km/hr**

**Initial speed =14/3×15/14 = 5 km/hr.**

**5.The length of the minutes hand of a clock is 8cm. Find the distance travelled by its outer end in 15 minutes.**

**(a) 4 πcm**

(b) 8 πcm

(c) 12 πcm

(d) 16 πcm

(e) None of the above

**Distance travelled by the end of minutes hand =2πr/4**

**=(2 × π × 8)/4=4πcm**

**6.A man walked at a speed of 4 km/h from point A to B and came back from point B to A at the speed of 6 km/h what would be ratio of time taken by the man in walking from point A to B to that from point B to A:**

(a) 5: 3

(b) 2: 3

**(c) 3: 2**

(d) 4: 3

**When distance is constant**

**S∝1/T**

**S1/S2 =T2/T1**

**T1/T2 =6/4**

**T1/T2 =3/2**

**T1 ∶T2=3∶2**

**7.Two train 130 m and 110 m long, while going in the same direction. The faster train take one minute to pass the completely. If they are moving in opposite direction, they cross each other completely in 3 seconds. Find the speed of each train:**

**(a) 42 m/s, 38 m/s**

(b) 38 m/s, 36 m/s

(c) 36 m/s, 44 m/s

(d) None of these

**Let, speed of faster trim S_1 m/s**

**Speed of slower train =S_2 m/s**

**S1-S2=(130+110)/(1×60)**

**= 4 m/s**

**S1+S2=(130+110)/3=80**

**S1=42 m/s**

**S2=38 m/s**

**8.A boy started from his house by bicycle at 10:00 am at a speed of 12 km/h. His elder brother started after 1 hour 15 minute by scooter**

**along the same path and caught him at 1: 30 pm. The speed of scooter was (in km/h):**

(a) 4.5

(b) 36

**(c) 18 2/3**

(d) 9

**Distance covered by cycling in 1 1/4 hr = 12 + 12×1/4 = 15 km**

**Elder brother catch the boy = in 2 1/4 hr**

**Now, according to question**

**(Scooter)_(Speed )-(Cycling)_Speed=15/(2 1/4)**

**(Scooter)_(speed )=(15 × 4)/9+12**

**=20/3+12**

**=56/3=18 2/3**

**9.A man is walking at a speed of 10 km/h. After every km. he takes a rest for 5 minutes. How much time will he take to cover a distance of 5 km:**

(a) 60 minutes

**(b) 50 minutes**

(c) 40 minutes

(d) 70 minutes

**Time taken in covering 5 km**

**=5/10=1/2 hr = 30 minutes**

**That person will take rest for four times.**

**Required time = (30 + 4 × 5) = 50 minutes**

**10.The fare of a bus is Rs. x for the first five kilometers and Rs 13 per km thereafter. If a passenger pays Rs. 2402 for journey of 187 km. What is the value of x?**

(a) 29

(b) 39

**(c) 36**

(d) None of these

**Required equation,**

**x + 182 × 13 = 2402**

**x = 2402 – 2366**

**x = 36**