A man has given one -fourth part of his property to his daughter half part to his sons and one fifth part given as charity. How much part of his his property he has given?

Let the positive number be N.
According to the question,
N + 10 = 200 / N
? N² + 10N = 200
? N² +10N - 200 =0
? (N - 10)(N + 20) = 0
? N = 10 & N= -20
But N not equal to -20 since N is a positive number
So, the required number is 10

Let the number be N.
According to the question,
N - (N x 3/4) =163
? N/4 =163
? N=652

Given Exp. = 6/7 + [(y - x)/(y + x)]
= 6/7 + [1 - (x/y) / 1 + (x/y)]
= 6/7 + [1 - (3/4)] / [1 + (3/4)]
= 6/7 + 1/7 =1.

Let 62976/N = 123
Then N = 62976 / 123 = 512.

Let 4050/?N = 450
Then ?N = 4050/450 = 9
? N = (9 x 9) = 81.

Let the number be a and b Then
a + b = 10 ..........(i)
ab = 20 ........(ii)

Sum of reciprocal = 1/a + 1/b
= (a + b) / ab
= 10/20
= 1/2

the number of pieces of chocolate left with manju =1- [(1/4) + (1/3) + (1/6)]
= 1 - [ (3 + 4 + 2)/12)
= 1 - (9/12)
= 3/12
Hence number of piece of chocolate left with in manju is 3

Factors of composite number = (P₁ +1)(P₂+1)(P₃+1)......(P_n+1).
Where P₁,P₂,P₃... P_n are the powers of respective prime factors.

So,
120= 2³ x 3¹ x 5¹
Factors=(3+1)(1+1)(1+1)=16.

Solving the question by taking two odd numbers greater than 1 i.e. 3 and 5,
for n =3, n( n² -1 ) = 3( 9 - 1) = 24
for n = 5 n( n² -1 ) = 5( 25 - 1) = 120

Using option we find that both the number are divisible by 24.

For n =1
7⁶ⁿ - 6⁶ⁿ = 7⁶ - 6⁶
? ( 7³ )² - ( 6³ )²
? ( 7³ - 6³ )( 7³ + 6³ )
= ( 343 - 216 )( 343 + 216 )
= 127 x 559

? it is clearly divisible by 127.