The sum of squares of two numbers is 68 and the squares of their difference is 36. The product of the two number is?

Let the required fraction be p/q.
Then, (p +1) / (q +1) = 4
? p - 4q= 3 ....(i)

And, (p - 1) / (q -1) = 7
? p - 7q = -6 ....(ii)

Solving these equation we get p = 15, q=3

Let unit digit = x and ten's digit = y
3(x + y)= 10y + x .....(i)
10y + x + 45 = 10x + y ....(ii)

2x - 7y = 0.9x -9y = 45
or x - y = 5 .... (iii)

Solving these equations, we get
x=7, y=2
? Required number = 27

Let second number be 3N, then, first one is 6N and the third one is 2N.
From question 3N + 6N + 2N = 132
? 11N = 132
? N = 12

? Second number = 3N = 3 x 12 = 36

Let the value for ? be N
So N x 9 x 7 x 3 = a number with unit digit 1.
Clearly, the minimum value of N is 9.

Let x/5 = p and let y when divided by 5 gives q as quotient and 1 as remainder.
Then, y = 5q + 1
Now x = 5p and y = 5q + 1
? x + y = 5p + 5q + 1 = 5(p + q) + 1
So, required remainder = 1

Let the numbers be x and y ,
Then, 2x + 3y = 18 ....(i),
3x + 2y = 17 ....(ii)

Solving, we get x =3 , y= 4
? Largest number = 4

Let the number be x, y, z
Then,
x + y = 45,
y + z = 55,
z + 3x = 30

Now, y = (45 - x) and
z = 55 - y
? z = 55 - (45 - x ) = 10 + x

? 10 + x + 3x = 90
? x = 20
So, third number = z
= 10 + x = 30

The number is of the form (5x + 3 ) where x is an integer

? [(5x + 3)²] / 5 = ( 25x² + 30x + 9) / 5
= 25x²/ 5 + 30x/5 + (5 +4)/5
? The remainder is 4.

According to the question
Divisor = 2/3 x dividend
and Divisor = 2 x remainder
or 2/3 x dividend = 2 x 5
? Dividend = 2 x 5 x 3 / 2 = 15

Number of one digit pages from
1 to 9 = 9
Number of two digit pages from
10 to 99 = 90
Number of three digit pages from
100 to 200 = 101
? Total number of required figures
= 9 x 1 + 90 x 2 + 101 x 3 = 492