GIST Institute
TIME AND DISTANCE SHORTCUTS
Formula:
Distance = Speed x TimeTime = Distance / Speed
Speed = Distance / Time
Important Point to be taken care of:
To convert speed in kmph to m/sec, multiply it with 5/18To convert speed in m/sec to kmph , multiply it with 18/5.
Example
1. If a men travels from point A to point B with a speed of 'a' and back to point A (from point B) with a speed of b, then the average speed of the body is:
2ab/(a+b).
A car covers a certain distance at a speed of 90 km/hr while going and returns to the starting point at a speed of 60 km/hr. Find the average speed of the car for the whole journey?Ans: Average speed = (2 x 90 x 60)/ (60+90)
= 72 km/hr
.
2. If a car does a journey in 'T' hrs, the first half at 'a' km/hr and the second half at 'b' km/hr. The total distance covered by the car:
(2 x Time x a x b ) / (a + b).
A motorcar does a journey in 10 hrs, the first half at 21 kmph and the second half at 24 kmph. Find the distance?Ans: Distance = (2 x 10 x 21 x 24) / (21+24)
= 10080 / 45
= 224 km.
3.If a person goes from 'A' to 'B' at a speed of 'a' kmph and returns at a speed of 'b' kmph and takes 'T' hours in all, then the distance between the A and B:
Total time taken x (Product of the two Speeds / Addition of the two speeds)
A boy goes to school at a speed of 3 kmph and returns to the village at a speed of 2 kmph. If he takes 5 hrs in all, what is the distance between the village and the school?
Ans: Let the required distance be x km.
Then time taken during the first journey = x/3 hr.
and time taken during the second journey = x/2 hr.
x/3 + x/2 = 5 => (2x + 3x) / 6 = 5
=> 5x = 30.
=> x = 6
Required distance = 6 km.
4: Walking ¾ of his speed, a person is 10 min late to his office. Find his usual time to cover the distance?
Ans: Usual time = Late time / {1/ (3/4) - 1)
= 10 / (4/3 -1 )
= 10 / (1/3)
= 30 minutes.
5: Running 4/3 of his usual speed, a person improves his timing by 10 minutes. Find his usual timing by 10 minutes. Find his usual time to cover the distance?
Ans: Usual time = Improved time / { 1 - (1/ (3/4)}
= 10 / { 1- (3/4) }
= 40 minutes.
6 A train travelling 25 kmph leaves Delhi at 9 a.m. and another train travelling 35 kmph starts at 2 p.m. in the same direction. How many km from will they be together ?
Ans: Meeting point's distance from the starting point = [25 x 35 x (2p.m. - 9 a.m)] / (35 -25)
= (25 x 35x 5) / 10
= 4375 / 10
= 437.5 km .
Percentage shortcuts and tricks
by a certain percent , we means that many hundredths thus , x percent means x hundredths written as x%
Fraction value of percentage :
1/2 = 50 % 1/3 = 33.33% 1/4 = 25% 1/5 = 20 %
1/6 =16.67% 1/7 = 14.28% 1/8 =12.5% 1/9 = 11.11
Note :these fraction value helps to minimize the calculation
Formula:
- if the price of a commodity increases by R% , then the reduction in consumption so as not to increase the expenditure is 100*R/(100+R)%.
- if the price of a commodity decreases by R% , then the increases n consumption so as not to decreases the expenditure is 100*R/(100-R)%.
- value of machine after n years = p(1-R/100)power n .
- if A is R% more than B , then b is less than A by 100*R/(100+R)%.
- if A is R% less than B , then b is more than A by 100*R/(100-R)%.
Example:
1. if 1/5 of a number is 25 less then 1/4 of a same number . what will be 3/2 of number .
ans.
as you know 1/5 = 20% and 1/4 = 25%
so difference b/w these two is 5% which is equal to 25
then 5% *20 ---- 25*20 100% ----500
and 100% percent is the real value
you can now calculate 3/2 so ans is 750
you can now calculate 3/2 so ans is 750
2. if the numerator of fraction is increase by 20% and denominator is decrease by 80% then fraction becomes 18/15. what is the actual fraction .
ans . 120% N/20% D = 18/15
then N/D = (18/15 )*20/120
N/D = 1/5 answer
3 . if A's salary 20% less then B's salary then B's salary is how much more then A.
ans . suppose B's salary is 100 then A's salary is 80
now you can calculate b's salary in respect to A
( 20/80)* 100 = 25% is answer
formula for this problem % change = (x)+(y)+x*y/100
Note take the value with symbol , if increase then take '"plus" if decease in value then take "minus". this formula is applicable for circle , square , triangle etc
12- 18 - 216/100 = -8.16 decrease is value by 8.16%
Partnership shortcuts and tricks
Partnership is an association of two or more persons who put their money together in order to carry on a certain business.
It is of two kind:
It is of two kind:
- Simple
- Compound
Tricks & Formula
A’s capital*A’s time in partnership A’s Profit
………………………………….................... = ……………
B’s capital*B’s time in partnership B’s Profit
Example:
Manoj and raj enter into a speculation. Manoj puts in rs. 50 and raj puts in rs. 45 at the end of 4 months manoj withdraws half of his capitals. Piyush then enter with capital of rs. 70 . at the end of 12 month in what ratio will the profit be divided.
= 50*4+25*8 : 45*6+45*6:70*8
= 400:405:560
=80:81:112--------------------------------------------
Maths - short cut tricks for square
In this post you learn some shortcut method related to square of number.here I will explain Some Tricks that improve your speed during calculation.
Trick 1: 2 Digit Number which ends in 5
Step 1: Multiply ten’s digit with its next number.Step 2: Find square of unit’s digit. i.e.: Square of 5.
Step 3: Write answers of step 1 and step 2 to together or side by side.
Let’s take examples. Find square of 45
Step 1: => 4 × ( 4 + 1 ) = 4 × 5 = 20
Step 2: = > 25 ( square of unit’s digit)
Step 3: => (step 1) ( step 2) Answer = 2025
Step 2: Multiply the number being squared by 2 and subtract 1.
Step 3: Add Step 1 and Step 2
Find square of 31.
Step 1 = > 302 = 900
Step 2 = > (31 × 2) – 1 = 62 – 1 = 61
Step 3 = > 900 + 61 = 961
So B is units digit and A is tens digit.
Step 1: Find Square of B
Step 2: Find 2×A×B
Step 3: Find Square of A
Step 1: => 4 × ( 4 + 1 ) = 4 × 5 = 20
Step 2: = > 25 ( square of unit’s digit)
Step 3: => (step 1) ( step 2) Answer = 2025
Trick 2 : if you know square of the previous number.
Step 1: Find square of the previous number which is known.Step 2: Multiply the number being squared by 2 and subtract 1.
Step 3: Add Step 1 and Step 2
Find square of 31.
Step 1 = > 302 = 900
Step 2 = > (31 × 2) – 1 = 62 – 1 = 61
Step 3 = > 900 + 61 = 961
Trick 3 : Any two digit number square
Let’s say the number is two digit number. i.e. AB.So B is units digit and A is tens digit.
Step 1: Find Square of B
Step 2: Find 2×A×B
Step 3: Find Square of A
Step 4 :Add carry from brackets right to left
(n1n2)^2 = (n1)^2(2xn1xn2)(n2)^2
eg:
(42)^2 = (4)^2(2x4x2)(2)^2 = (16)(16)(4)
Let’s take an example.
We want to find square of 37.
Step 1: Find square of 7. Square of 7 = 49. So write 9 in the answer and 4 as carry to the second step.
Step 2: Find 2×(3×7)
2 × (3 × 7) = 42.
42 + 4(Carry) = 46.
42 + 4(Carry) = 46.
Step 3: Find square of 3
Square of 3 = 9
9 + 4(Carry) = 13.
Write 13 in the answer.
9 + 4(Carry) = 13.
Write 13 in the answer.
So the answer is 1369.
Basically in math form you can say(n1n2)^2 = (n1)^2(2xn1xn2)(n2)^2
eg:
(42)^2 = (4)^2(2x4x2)(2)^2 = (16)(16)(4)
= > add carry from brackets right to left
= (17)(6)(4) = 1764
Trick 4 : Square for number From 31 to 50:
Find the square of 38.
Step 1 : 12 =50-38
Step 2 : Last 2 Digit : Square of 12 = 144 =44 (1 Carry)
Step 3 : First 2 Digit: 25-12+1 =14
Step 1 : 12 =50-38
Step 2 : Last 2 Digit : Square of 12 = 144 =44 (1 Carry)
Step 3 : First 2 Digit: 25-12+1 =14
Final answer =1444 (First 2 Digit Last 2 Digit)
382=1444
Step 1 : 50+12 ( Yes, every time You have to think like this 50 + )
{If the number is 72 We will write 50+22}
Step 2 : Last 2 Digit : Square of 12 =144 = 44 ( 1 will be carry )
Step 3 : First 2 Digit : 25+12+1 =38
25 is constant number for every number 51-80 You have to add this!!
So our final result is 3844 (See First 2 Digit and Last 2 Digit above)
622 = 3844
382=1444
Trick 5 : Square for number From 51 to 80:
Find the Square of 62Step 1 : 50+12 ( Yes, every time You have to think like this 50 + )
{If the number is 72 We will write 50+22}
Step 2 : Last 2 Digit : Square of 12 =144 = 44 ( 1 will be carry )
Step 3 : First 2 Digit : 25+12+1 =38
25 is constant number for every number 51-80 You have to add this!!
So our final result is 3844 (See First 2 Digit and Last 2 Digit above)
622 = 3844
Trick 6 : Square for number From 81 to 100:
Find the square of 88Step 1 : 88=100 -12 ( Yes 100-12 Only , not 50+38 or 80+8 )
{If the number is 92 then we have to think like 100-8}
Step 2 : Last 2 Digit : 122 = 144 = 44 (1 carry )
Step 3 : First 2 Digit : 88 - 12 + 1 =77
So our final Answer is 7744 (First 2 Digit Last 2 Digit)
You can also share your trick on comment.
