Quant Boosters  Maneesh  Set 1

Q27) Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first met after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters ?

Let length is x.
At first meeting point, Brenda runs 100 meters and sally runs (x/2) – 100
At second meeting point, Sally runs 150 meters and Brenda runs x150 meters
100/x150 = (x/2) 100/150
15000 = x^2/2100x 75x+15000
x^2/2 – 175x = 0
x^2350x = 0
x = 350 meters.

Q28) A and B start from same point on the circular track in same direction. A completes a track in 7 minutes and B takes 3 minutes. When they started running it was 12.00 PM by clock. When they meet 4th time what is time by clock?

If A and B takes m and n minutes respectively to complete one circular track then A and B would meet for the first time after
T = (m * n) /mn
They will keep meeting at the interval T.
m = 7 n= 3
T = 21/4 minutes
4th time it will take 4T = > 4 * 21/4 = 21 minutes
So time 12:21

Q29) Vijay left P for Q at 10:00 AM. At the same time Ajay left Q for P. After their meeting on a point on the way Vijay took 24 minute to reach Q and Ajay took 54 minute to reach P. At what time they met?

Speed of Vijay/Speed of Ajay = root (54/24) = root (9/4) = 3/2
Distance = 3x*24/60 + 2x * 54/60 = 180x/60 = 3x
Time taken to meet = 3x/5x = 3/5 = 36/60
= > after 36 minutes …that is 10:36

Q30) A fires two bullets from same place at an interval of 6 minutes but B sitting in a car approaching the place of firing hears the second fire 5 minutes 32 seconds after the first firing. What is the speed of the car if speed of sound is 332m/s?

It took 28 seconds for him to travel from the place where he heard sound first to current place.
Distance (sound) = 28 *332 m
Same distance he travelled in 5 minutes 32 seconds.
Speed of car = 28 * 332/332 = 28 m/s

LCM (9,18,24) = 72
9  5 = 18  14 = 24  20 = 4
Since difference is same , answer will be LCM – common difference = 724 = 68

At first ON > 8/3 16/3 14/3 15/2
Each word is put off after a second
So Om will flash after > 8/3+1 = 11/3 seconds
Similarly Innovative > 19/3
Book > 17/3
Store > 15/2 + 1 = 17/2
So all will together after LCM [ 11/3 , 19/3, 17/3,17/2] = 11 * 19 * 17 = 3553 SEC