If a number is multiplied by three-forth of itself. The value thus obtained is 10800. What is that number?

Let quotient = Q and remainder = R
Then, Divisor = 12 Q =5 R
Now, R = 48
? 12Q = 5 x 48
? Q = 20

Dividend = Divisor x Quotient + Remainder
? dividend = ( 20 x 240 + 48 )
= 4848

Required number is 2 x 4 x 6 = 48.

Let 10/11 = 110/N,
Then, 10N = 11 x 110
? N = (11 x 110) /10 = 121.

The first prime number is 2.

First four prime numbers are 2,3,5,7,
Their sum = (2 + 3 + 5 + 7) = 17.

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

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

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.

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

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.