Let’s suppose there is ‘n’ number of persons are there and each one suppose to do an handshake with ‘n-1 persons.
So, Total number of handshakes is = n(n-1) (with repetition)
But we need without repetition means distant handshakes (A→ B, B → A) so we divided by ‘2’
= n(n-1) / 2
= 5(5-1) / 2
= 10

Let’s take length of the train = ‘x’
Speed of the Train = 60km/hr and crosses a pole in 9 Seconds.
Speed of the train is km/hr and crosses a pole in seconds.
So we need to convert the km/hr into mts /sec.
For that one we need to multiply the speed of the train to (5/18).
Speed of the train = 60 * (5/18)
We have one Basic formula in Time and Distance
Distance = Speed * Time
x = 60 * (5/18) * 9
x = 150 mts

For this Problem, We need two important formulas.
1. %Profit = ((Selling Price - Cost Price) / (Cost Price) ) * 100
2. %Loss = ((Cost Price - Selling Price) / (Cost Price)) * 100
From the above question we know
% Profit = % Loss
Selling price when they got profit = 1920 /-
Selling price when they got loss = 1280 /-
((1920 - Cost Price ) / ( Cost Price) ) * 100 = (( Cost Price - 1280 ) / (Cost Price)) * 100
After Solving this
2 * Cost Price = 3200
Cost Price = 1600
We got cost price, Now we need to find out Selling price when they got 25% Profit
Cost Price = 1600
Profit% = 25
Selling Price = ?
%Profit = ((Selling Price - Cost Price) / (Cost Price) ) * 100
25 = ((Selling Price - 1600) / 1600)) * 100
25 * 16 = Selling Price - 1600
Selling Price = 1600 + 400
Selling Price = 2000/-

Speed of the Down Stream = 2 km/ 1 = 2 km/hr
Speed of the Upstream = 5km / (10/60) = 6km/hr
Speed of the Boat still in water = (Downstream + Upstream ) / 2 = (6 + 2) / 2
= 4 km/hr
Time taken for 5 km in Stationary water = 5/4 = 1(1⁄4)
= 1Hr 15 Min

Present age of 3 persons is = 4x, 7x, 9x
Eight years ago their sum is = 56
So,
4x+7x+9x-(8+8+8) = 56 (Eight Years Ago so that we subtract their individual ages from present age)
20x = 80
x = 4
Present ages = 4 * 4 , 7*4, 9*4
= 16, 28, 36

Let’s take the first pipe to a fill a tank in ‘x’ hours.
So, from that question we know that second pipe fills a tank 5 hours faster than 1st pipe means second pipe fills a tank in ‘x/5’ hours.
And Second pipe fills a tank 4 hours slower than third pipe means third pipe can fill a tank in ‘x/20’ hours.
The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone.
(1 / x) + (5 / x) = (20 / x)
x = 15 Hours

Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 680
Breadth = 34 feet
Area to be fenced = 2B + L = 2 (34) + 20 = 88 feet

In ‘CORPORATION’ We have total 5 vowels (OOAIO) and taken has one unit
Remaining Consonants are (CRPRTN) 6 and add vowels unit 1.
6 + 1 = 7 In this R is repeated 2 times
In ‘CORPORATION’ We have total 5 vowels (OOAIO) and taken has one unit Remaining Consonants are (CRPRTN) 6 and add vowels unit 1. 6 + 1 = 7 In this R is repeated 2 times So number of ways we can arrange these words = 7! / 2! = 2520
number of ways we can arrange vowels is 5!
2 ‘O’ are repeated so 5! / 2! = 20
Total Number ways = 2520 * 20 = 50400
So number of ways we can arrange these words = 7! / 2! = 2520
number of ways we can arrange vowels is 5!
2 ‘O’ are repeated so 5! / 2! = 20
Total Number ways = 2520 * 20 = 50400

Seats for Mathematics, Physics and Biology in a school are in the ratio is 5:7:8.
There is a proposal to increase these seats by 40%, 50% and 75% respectively means
After increasing seats ratio will be
5 * (140/100) : 7 * (150/100) : 8 * (175/100)
5 * 140 : 7 * 150 : 8 * 175
28 : 42 : 56
2 : 3 : 4

Let’s take height of the building is x.
From that question we know that less height less shadow so it’s directly proportional.
40.25 : 17.5 : : 28.75 : x
x = (17.5 * 28.75) / 40.25
x = 12.5 m

Except 427 remaining numbers are sum of first number and last number is middle number.

From the above sequence we know that
2 + 3 = 5
5 + 5 = 10
10 + 7 =17
17 + 9 = 26
26 + 11 = 37
37 + 13 = 50
50 + 15 = 65 But in the question they given 64. So 64 is wrong.

The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum is = p * (R/100)^2
P * (R/100)^2 = 1
P * (4/100)^2 = 1
P * (1/25)^2 = 1
P = 625
So, Sum is 625

For this type of questions we have to find gcd of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
So, = H.C.F. of 3360, 2240 and 5600 = 1120.
sum = 1+1+2+0 = 4.