### Answers:-

*Q1. Option C*

*Differences in Time taken for both movements are same here. So,*

*Speed = 2* (increased speed)*(decreased speed) /difference in speed*

*= 2*8*4 /8- 4*

*= 2*8*4/4*

*= 16kmph*

* *

*Q2. Option D*

*Difference in time taken =40-30= 10min = 10/60 = 1/6 hr*

*Speed during the next journey= 15+3 =18kmph*

*So time taken, x/15 –x/18 = 1/6*

*3x/ (15*18) =1/6*

*X / (5*18) = 1/6*

*x = (18*5)/6*

*Distance (X) = 15km*

* *

*Q3 Option C*

*Let assume the usual speed of the train X kmph*

*Then, 75% of usual speed = 75*x/100 =3x/4*

*Now, L /x = 12*

*L = 12x*

*Again, (L+450) /(3x/4) =18*

*12x+450 = 18*(3x/4)*

*450+ 12x = 27x/2*

*450+12x = 13.5x*

*1.5x = 450*

*X = 450/1.5 =675m*

*Speed = 18*(5/18) = 5m/s;*

*Time taken = Distance /Speed = 675/5= 135 Seconds*

*=> 135/60 min = 2 hr 15 min*

* *

*Q4. Option B
*

* *

*Q5 Option C
Let the distance between Coimbatore and Ahmadabad be X*

*Speed of first train= x/4 km/h*

*Speed of second train =x/3 km/h*

*Let they meet y hrs after 7.00am*

*Then, according to the question,*

*X/4 *y +x/3 * (y-2) =X*

*Y/4 +(y-2)/3 =1*

*3y+4(y-2) =12*

*3y+4y-8 =12*

*7y=20*

*Y=20/7*

*Y =2 hrs 51 min 25 sec*

*Two trains cross each other = 7+2.51 = 9.51 am(approx)*

* *

*Q6 Option A*

*Let the length of train B be X m.*

*Then, length train A =2X/5*

*Now the speed of train B to that of train A = (X/70): (2X/5 /45)*

*= (70/x) *(2x/225)*

*= 140: 225 = 28:45*

* *

*Q7 Option C
Speed of the truck= D/T = 294/7 = 42km/hr*

*Now, Speed of car = (Speed of truck +14) km/hr = 42+14 = 56km/hr*

*Distance of car = 294+16 = 310 km*

*Time Taken = 310/56 = 5hr 32 min*

* *

*Q8 Option B*

*Relative speed = (65.5 /35) *60 = 786/7 kmph*

*Speed of A = 786/7 -45 = 471/7 = 67.28 kmph*

* *

*Q9 Option B*

*D=78km; a=16kmph, b=10kmph*

*According to the formula,*

*Distance travelled by*

*R = AC =2D*(a/a+b)*

*= 2*78 *(16/ (10+16))*

*= 2*78 *(16/26)*

*= 2*78*(8/13) =96km*

* *

*Q10 Option C
Express:*

*Time taken to cover 75km (including stoppage) = 30min+6min =36min*

*Time taken to cover the total distance by Express= (36/75*825) +36min = 432min*

*Local Train:*

*Time taken to cover 37.5km (including stoppage) = 30min+2min =32min*

*In 32min, distance covered =37.5km*

*Required total distance = 432*(37.5/32)= 506.25km*