Quiz 1

m*d*t/w=m1*d1*t1/w so 3/50=6*x/300 ans is x= 300*3/50*6

x=3

speed1=48km/hr and time1=50/60hr
distance=speed*time
distance=48*50/60=40km
now it is given that the distance remains same but
she has to win the race in 40 min
therefore now:
time2=40/60 hr and distance=40km
speed2=40/(40/60)=40*60/40=60 km/hr

m1 * d1 = m2 * d2
3 *4 = 4 * x
where x = no. of days taken by 4 men to paint

Therefore, x=3

let from his home to station distance = x
so,
(x/40) + ((52-x)/80) = 1
solving this x = 28 km
so from office to station = 52-x = 52-28 = 24 km

When B is given a 40 m start then B runs 960m in T secs and A runs 1000m in T-19 secs.
When B is given a 30 second start then B runs 1000m in t secs and A runs 960m in t - 30 secs.
Assume that the speed of A (Va) and B (Vb) is constant in both situations.
Then Vb = 960 ÷ T = 1000 ÷ t, and Va = 1000 ÷ (T - 19) = 960 ÷ (t - 30)
So 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.
Substituting for t in 960t = 1000T
gives : -960T + 282240 = 1000T
1960T = 282240
T = 144
B 's speed is 960 / T = 960 / 144 = 6.67 metres per second.
Assuming the same constant speed to run 5000 metres then the time taken is
5000 / 6.67 = 750 seconds

let they meet t hours after 1 pm

the person from p moves 6/11 km in 1 hr so 3-6/11=27/11
6/11 t+5/22 t=27/11
17/22 t=27/11
t=54/17 =3.17h
so time=4:17 pm

let the speed is a & b (b>a)
total distance =x
two equation will form
18.5/a=(x-18.5)/b (Deep end equation)
x=18.5(a+b)/a..................1
also,
x/b+45+10.5/b=x/a+45+(x-10.5)/a (swallow end equation)
x=10.5(a+b)/(2a-b).........2
equating 1 & 2
we get a/b=37/53
so, x=18.5*90/37=45

if two trains of lengths a and b are moving towards each other
with speeds xkmph and ykmph respectively, then time taken
by them to cross each other= a+b/u+v
here t=9secs.
9=x+270/120+80 (assuming second train length as x)
9=x+270/200*5/18 (converting kmph into m/s)
9=x+270/11.11*5
x=229.95=230

train and man ismoving in the same direction so the
relative speed will be= (63-3)km/hr
= 60km/hr
then 60km/hr * 5/18= 50/3 m/sec
therefore, time = distance/speed
= 500/ (50/3)
= 30 seconds
so the answer is 30 seconds

speep =distance/time
speed of first train
5x =350/2=35kmph
x=35
therefore speed of second train is=3x=3*35=105kmph.