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 property he has given?

Let the number be N.
According to the question,
? 5N = 2N² - 3
? 2N² - 5N - 3 = 0
? (N - 3) ( 2N + 1 ) = 0
N = 3 and N = -1/2
Thus, the required number is 3.

Here, M + N = 10 and MN = 20
According to the question,
(1/M) + (1/N) = (M + N) / MN = 10/20 = 1/2

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
&ythere4; N = 10 and N = -20
But N ? -20, since N is a positive number.
So, the required number is 10.

Let the number be N
According to the question
N - 3N/4 = 163
? N/4 = 163
? N = 652

Let the two consecutive numbers are N and N+2

According to the question
N (N + 2) = 19043
? N² + 2N - 19043 = 0
? N² + 139N - 137N - 19043= 0
? N( N + 139) - 137 ( N - 137 ) = 0
? N( N + 139) ( N - 137) = 0
? N = 137 and N = - 139
? N = 137

The number of pieces of chocolate left with Manju
= 1- [(1/4) + (1/3) + (1/6)
= 1 - (3 + 4 + 2)/12
= 1 - 9/12 = (12 - 9) / 12
= 3/12

Let the number be N.
According to the question,
(N x 3)/2 - N / (3/2) = 10
? 3N/2 - 2N/3 = 10
? (9N - 4N) / 6 = 10
? 5N / 6 = 10
? N = (10 x 6)/5 = 12

Let √N/19 = 4
Then √N = 19 x 4 = 76
∴ N = 76 x 76 = 5776.

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

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