Q1-Rahul when increase his speed from 24 km/h to 30 km/h .he takes one hour less than the usual time to cover a certain distance . what is the distance usually covered by Rahul?

Simple question and can be easily solved using traditional method . but using percentage and ratio concept such type of questions you solve without use pen and paper.
let's begin ,
before apply percentage concept ,you must know the method how to convert percentage to fraction quickly [ percentage part-3,you go and learn this method first ]
in time distance problem 90% even more than that problem are based on ratio concept .let you go to market at 15 km/h and take 5 hour to reach the market . what distance you cover in 5 hour .any formula required to find the distance ,no just multiplied 15*5=75 km . if you understand that term . it adequate to solve all the problem.

solution - rahul increase his speed 24 to 30 km/h . here distance is constant .so 24 to 30 ,increase in speed is 25% .[ 6/24=1/4=25%]
5/4 speed increase .then time is inversely proportion of time .time decrease 4/5 [ if distance constant ,you increase your speed then what will be effect on time.naturally your time will be decrease ,logically think do not need to remember anything .]
now rahul take 4 hour to cover the distance so 4*30=120 km answer.

second method- you find the ratio of speed ,24::30
=4:5
so time ratio will be
=5:4
distance = either you multiplied 4*30 or 5*24 it gives you same result .

third method- go through option .which option multiple of 24 and 30 .its your answer .or check divide the option one by one .if time difference is equal to 1 hour .then mark the answer directly [ in this chapter 50% questions solve through option] lots of way to solve this problem .

2-A train met with an accident 60 km away from the Delhi station . it completed the remaining journey at 5/6 of the previous speed and reached the Kanpur station 1 hour 12 minute late .had the accident taken place 60 km further , it would have been only one hour late .
1-what is the normal speed of train ?
2-what is the distance between Delhi to Kanpur ?
Please solve this question and comment your approach . after that i show you how to solve this type of questions mentally .

Q3-Rahul leaves Patna at 6 am and reaches Hajipur at 10 pm . Gopal leaves Hajipur at 8 am and reaches Patna at 11.30 am . at what time do they cross each other ?

1-10 am 2- 8.32 am 3- 8.56 am 4- 9.20 am

how many of you able to solve this question mentally . do not wary about it .if you here then for sure learn something new .just wait

first you understand what is the constant in ,this question .
here distance is constant .
rahul take 4 hour to complete the journey . but gopal take 3.5 hour for it .
so ratio of speed is inverse the ratio of time
ratio of time is rahul to gopal =4:3.5
=40:35
=8:7, so speed ratio equal to 7:8 [ you are very good in ratio directly say 8.56 am they cross each other ]
please understand what i m try to say ,
rahul speed is 7 km/h and gopal speed is 8 km/h .
rahul take 4 hr to complete the journey ,therefore in two hour he complete half of journey .tell me what is the total distance covered by rahul in 4 hour at speed of 7 km/h . 28 km . at 8 am rahul covered 14 km total distance .[ always try to make the time equal ]
remaining 14 km covered by both then they meet at certain point . 14/15*60=56 mint .so 8.56 am they cross each other .if you join our class and learn the ratio concept after that without knowing the actual concept about this chapter ,you solve this question in 10 second .i grantee it . many way to solve this question but here i just try to teach you concept behind this this chapter. once you understand the concept ,nothing will be left for you .just understand the concept .

4-A and B travel the same distance at 9 km/h and 10 km/h respectively . if A takes 20 minutes longer than B , the distance traveled by each is :

solve this question with the help of above concept .

Q5- A train approaches a tunnel AB. inside the tunnel a cat located at a point i.e 5/12 of the distance AB measured from the entrance A. when the train whistles , the cat runs .if the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance . if the cat moves to the exit B , the train catches the cat at exactly the exit .the speed of the train is greater than the speed of the cat by what order ?

initially this question looks very lengthy but once you understand the concept , reality is far away from that .

solution .
TRAIN ---------------------A------------------CAT-------------------------B
<----X----------><-------5-----><----------7---------->
I Never suggest to assume any variable . but we use only convenient for you . instead of X you use any constant like 6, 7 ,8 .but its need some basic ratio concept .any way let's move .

if you observed question carefully , then you say here time is constant . [ you read our first concept book .if not able to understand that term ]

time is constant , then ratio of speed is equal to ratio of distance [ don't mug up just spend some time to think over it ]
ratio of speed cat: train =distance traveled by cat : distance covered by train
=5/X=7/12+X
=x=30 . so speed ratio =30:5
=6:1 answer [ any doubt regarding this question please comment ]

in next part we teach you some more basic term , relative speed , boat and stream .. stay with us .thanks