12-09-2020
Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level),
Number System and NumberSeries
Natural Numbers N={1,2,3,4,…..}
Whole numbers W={0,1,2,3,4,…..}
Integers Z={…..-3,-2,-1,0,1,2,3,4,…..}
Rational Numbers Q= numbers which can be expressed in the p/q form
Irrational Numbers Q’= Numbers which cannot be expressed in p/q form
Imaginary Numbers =I= square root of all negative numbers
HCF and LCM of Numbers
HCF – Highest Common Factor
LCM -Least Common Multiple
Q)Four bells ring at intervals of 4, 6, 8 and 14 seconds. They start ringing simultaneously at 12.00 O’ clock. At what time will they again ring simultaneously?
Explanation-“They start ringing simultaneously” means they will meet at a common point after some time. and LCM that is Least Common Multiple will do the job.
Here you just need to take the LCM of the terms 4,6,8,14
and it will come out to be 168.
So, after 168 seconds they will ring, now converting 168 sec to minutes and seconds format it will be
2 minutes and 48 secs
Adding this to 12:00:00 we will get 12:02:48.
Q2)Three bells toll every 30 minutes, 45 minutes and 60 minutes. If they toll together at 9:30 am, what is the next time they toll together?
Explanation- LCM of 30,45,60 is 180
So, they will toll together after 180 minutes or 3 hours i.e.12.30 pm
Average
AVERAGE SPEED FORMULA
Average speed formula is used to find the uniform rate which involves something travelling at fixed and steady pace.
For example, A car travels 3 hours. It travels 30 miles in the first hour, 45 miles in the second hour and 75 miles in the third hour.
Speed in the first hour = 30 miles / hour
Speed in the second hour = 45 miles / hour
Speed in the third hour = 75 miles / hour
We have three different speeds in the three hour journey.
If we want to find the average speed for the whole journey of three hours, we have to find the ratio between the total distance covered and total time taken.
That is, constant speed = (30 + 45 + 75) / 3
= 150 / 3
= 50 miles / hour
Based on the above example, the formula is to find the average speed is given below.
Time and work questions:
UPSC generally asks time and work questions. You can solve them using these basic tricks.
- If A takes 5 days to complete a job and B takes 10 days, how many days will they take to finish the work together?
A does 1/5 of the work in 1 day.
B does 1/10 of the work in 1 day.
So together they will take 1/5 + 1/10 = 3/10 of the work in 1 day, i.e. 30% of the work in 1 day.
That means they will take 100/30 = 3.33 days to finish the work together.