# Quant Boosters - Soumya Chakraborty - Set 2

• This is a property of hm
If the hm of a and b is 'h'
Then the ratio of a:b is equal to the ratio of their differences from h
That is a/b = (a-h) /(h-b)

we know the ratio of speeds are 2:1 and their difference is 4
so the speeds are 8 and 4
usual speed is avg of these two = 6

HM for two numbers a & b = 2ab/(a + b)

There is a faster method

Find the HM of 30 and 50
Step 1: Take the ratio = 3:5
Step 2: Find the difference = 20
Step 3: Divide the difference in the above ratio = 3/8 * 20 & 5/8 * 20
HM = 30 + 3/8 * 20 = 37.5 or 50 - 3/8 * 20 = 37.5
This results from the property:
If HM(a,b) = h
Then (a - h)/(h - b) = a/b

• Q19) A vehicle travelling a certain distance, develops an engine trouble somewhere in between, thereby reducing the speed by 25%. Due to this, the vehicle reached the destination 50 minutes late. If, however, the engine trouble would've occurred 40 KM ahead, the would've reached the destination only half an hour late. Find the speed of the vehicle before the engine trouble. Also, find the sum of distances travelled by the vehicle in the two scenarios after the engine trouble occurred.

• Q20) A dog is stuck inside a tunnel AB, at a point P, such that AB = 5AP. The dog hears a train approaching towards the tunnel and start running towards B and just manages to escape. If, however, the dog would've ran towards A, it would have still managed to escape. Find the ratio of speeds of the train and that of the dog.

• Q21) A and B start from points P and Q travelling towards Q and P, respectively. If A takes 60 minutes to travel the entire distance and B takes 84 minutes to do the same, after how long did they meet?
(a) 30 minutes
(b) 32 minutes
(c) 35 minutes
(d) 40 minutes [CAT 2014]

• Q22) Ram was jogging towards beach one fine morning. He was travelling with a speed of 12 km/h. The distance to the beach was 24 km. There was a dog with Ram, who started running to and from between Ram and the beach till Ram reached the beach.
(1) What was the total distance run by the dog?
(2) What was the sum of distances run by the dig in the direction from Ram to the beach.

• Total Distance = 60 km
Distance run towards the beach = 42 km

• Q23) A person is travelling from Point P to point Q at a constant speed. Buses with equal speeds leave points P and Q (towards Q and P respectively) at same intervals. If a bus which is travelling from P to Q crosses the person every 60 minutes and a bus which is travelling the other way meets the person every 40 minutes, find the interval at which the buses ply from either points.
Details & Assumptions:
The interval at which buses start from either ends is same.
Buses MAY NOT start at the same time from point P and Q

• Q24) 5 buses start at different times from Point A towards Point B. Their speeds are in the ratio 1:2:3:4:6. All bus reach point B at the same time. If the fastest bus starts 10 hours after the one which started 2nd from Point A, find the time taken for the bus which started after 2 buses from Point A.

• Q25) A person travelling in a moving train hears 2 gunshots at an interval of 15 seconds. If, however, the two shots were fired actually at an interval of 18 seconds, find the speed of the train (Assume speed of sound = 330 m/s)

• Q26) Two people A and B starts jogging every morning from points P and Q, not necessarily at the same time, travelling towards Q and P respectively. Every day they meet at a point R, somewhere between P and Q. Speed of A = 10 km/h and Speed of B = 20 km/h.
a) One day, A starts 30 minutes later then the usual time. How much behind the point R, did A meet B?
b) The next day, A was on time, however B started 30 minutes later than its usual time. How much further the usual meeting point R, did A meet B?

• Answer is 3.33 for both questions

• Q27) Two cars start from point A at the same time every day, travelling towards point B via the same path. The faster car reaches point B 15 seconds earlier than the slower car. One day, the slower car starts 10 seconds early. the faster car, starting at the usual time, doubles its usual speed. The faster car again reaches 15 seconds earlier than the slower car. Find the speed ratio of the faster car to the slower car.

• Correct answer 7 : 4

• Q28) A boy can reach his school 20 minutes early if he increase his speed by 25%. How much time does he take to reach his school, travelling at his usual speed?

• Q29) A train after reaching exactly halfway to a platform that is double its own length, takes 40 s to cross the platform completely. How long will the train take to completely cross a bridge that is exactly 5 times the length of the platform ?

• Q30) The diagonals of a hexagon intersect at n distinct points inside the hexagon. What is the maximum value n can take ?

• Number of diagonals of a hexagon 6c2-6 = 9
Eliminating the intersections at vertices = 9c2 - 6 * 3c2 = 18
3 more cases has to be discarded...
Connecting (1,3) and connecting (4,6) won't intersect
Similarly 2 more..
So 18 - 3 = 15 is the answer

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