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
