In a group of equal number of cows and herdsmen, the number of legs was 28 less than four times the number of heads . The number of herdsmen was

Let us assume the ten's digit of the number is n. Then the unit's digit will be 3n.
According to question,
The sum of the digits is equal to 8.
sum of the digit = 8
n + 3n = 8
? 4n = 8
? n = 2
So, ten's digit is 2 and unit's digit is 6.
So the number = 10n + 3n = 10 x 2 + 3 x 2 = 20 + 6 = 26.

Let us assume the two digits number of the number is a and b.
According to given question,
The original number is 10a + b.
After interchanging the digits , the Number is 10b + a.
The number formed is greater than the the original number by 45,
We will get,
New number = Original number + 45
? 10b + a = 10a + b + 45
? 10b + a - 10a - b = 45
? 9b - 9a = 45
? b - a = 5
According the question the difference between the digits is 5 which will not help us to solve this question because both condition given in question are same. So can't be determined the answer.

Now try Hit and Trail method
Try one by one all option. All 3 Options are true.
But we cannot choose all 3 option, but as per question we cannot find the answer.

Let the ten's digits be x and unit's digit be y.
Then,(10x + y) - (10y + x)=36 ?9(x-y)=36
? x - y=4

Let us assume the first book published in year x.
According to question,
Books are published at seven years interval,
First edition book published in year = x
Second edition book published in year = x + 7
Third edition book published in year = x + 14
Four edition book published in year = x + 21
Five edition book published in year = x + 28
Six edition book published in year = x + 35
Seven edition book published in year = x + 42
When the seventh book was issued, the sum of the publication year was 13,524.
x + x + 7 + x +14 + x +21 + x + 28 + x + 35 + x + 42 =13524
147 + 7x = 13524
7x = 13524 -147
? x = 13377/7 = 1911
The first book published in year x = 1911

Let us assume the first number is x and second number is y.
According to question,
sum of twice the first number and thrice the second number is 100.
2x + 3y = 100 ...................(1)
and sum of thrice the first number and twice the second number is 120.
3x + 2y = 120...................(2)
Subtract equation (1) from Equation (2) after multiply 2 with Equation (1) and 3 with Equation (2), we will get.
3(3x + 2y) - 2(2x + 3y) = 3 x 120 - 2 x 100
9x + 6y - 4x - 6y = 360 - 200
5x = 160
x = 32
put the value of x in equation (1)
2 x 32 +3y = 100
3y = 100 - 64
3y = 36
y = 12
The larger Number is 32 .

Let us assume the number be N.
According to question,
A number when subtracted by 1/7 of itself gives the same value as the sum of all the angles of a triangle,
N - N x 1/7 = 180 ( As we know sum of all angels of a triangle is 180 .)
? N - N/7 = 180
? (7N - N)/7 = 180
? (7N - N) = 180 x 7
? 6N = 180 x 7
? N = 180 x 7/6
? N = 30 x 7
? N = 210

Let us assume the ten's place digit be x.
Then, the number = 10x + 3
and sum of digits = x + 3
According to question,
So, ( x + 3 ) = 1/7( 10x + 3 )
?7x + 21 =10x +3
? 3x = 18
? x = 6
The number = 10x + 3 = 10 x 6 + 3 = 60 + 3 = 63

Method 1 to solve the question.
Let us assume the numerator be x.
Then the denominator will be 3x + 2.
According the question,
if the numerator as well as denominator is increased by one , the fraction becomes 1/3,
(x + 1)/(3x + 2 + 1) = 1/3
? (x + 1)3 = 1(3x + 2 + 1)
? 3x + 3 = 3x + 3
Since Left hand side equation is same to right hand side equation. So we cannot solve the equation and cannot determine the answer.

Method 2 to solve the question.
Let us assume the numerator be x and denominator be y.
According to question,
The denominator of a fraction is 2 more than thrice its numerator.
y = 3x + 2 .....................(1)
Again According to question,
if the numerator as well as denominator is increased by one , the fraction becomes 1/3.
(x + 1)/(y + 1) = 1/3
? 3(x + 1) = y + 1
? 3x + 3 = y + 1
? y = 3x + 2............(2)
Since Equation (1) and (2) is same. So we cannot determine the number.

Method 3 to solve the question.
Hit and Trail method.
Solve all option one by one as per given question.
First took Option (A) 4/13
Numerator 4 in given fraction in Option (A)
The denominator of a fraction is 2 more than thrice its numerator.
So denominator = 2 + 4 x 3 = 2 + 12 = 14
So fraction will be 4/14 So this is wrong answer.
Now took Option (B) 3/11
Numerator 3 in given fraction in Option (B)
The denominator of a fraction is 2 more than thrice its numerator.
So denominator = 2 + 3 x 3 = 2 + 9 = 11
So fraction will be 3/11 So this is right answer.

Let us assume the two parts be y and (54 - y).
Then, According to question
10(54 - y) + 22y = 780
? 540 - 10y + 22y = 780
? 12y = 780 -540
? 12y = 240
? y = 20.
? Bigger part = (54 - y) = (54 - 20) = 34

Let number of notes of each denomination be N.
According to question,
A man has ?480 in the denominations of 1 rupee notes , 5 rupee notes and 10 rupee notes.
Total value of notes = 480
1 x N + 5 x N + 10 x N = 480
? N + 5N + 10N = 480
? 16N = 480
? N= 30.
Hence, total number of notes = 3N = 3 x 30 = 90