A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have?

Numbers from 1 to 60, which are divisible by 6 are : 6,12,18, 24, 30, 36,42, 48, 54, 60.

There are 10 such numbers.

Numbers from 1 to 60, the sum of whose digits is 6 are : 6, 15, 24, 33, 42, 51, 60.

There are 7 such numbers of which 4 are common to the above ones. So, there are 3such uncommon numbers.

Numbers from 1 to 60, which have 6 as one of the digits are 6, 16, 26, 36, 46, 56, 60.

Clearly, there are 4 such uncommon numbers.

So, numbers 'not connected with 6' = 60 - (10 + 3 + 4) = 43.

Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.

Let the number of spades be x. Then, number of clubs = (7 - x).

Number of diamonds = 2 x number of spades = 2x;

Number of hearts = 2 x number of diamonds = 4x.

Total number of cards = x + 2x + 4x + 7 - x = 6x + 7.

Therefore 6x + 7 = 13 ⟺ 6x = 6 ⟺ x - 1.

Hence, number of clubs = (7 - x) = 6.

Since the number of carbons is 2, only two copies can be obtained.

Let the father's age be x and the son's age be y.

Then, x - y = y or x = 2y,

Now, x = 36. So, 2y = 36 or y = 18.

Therefore Son's present age = 18 years.

So, son's age 5 years ago = 13 years.

Let the number be x. Then, x + 13x = 112 ⟺ 14x = 112 ⟺ x = 8.

Let the fixed charge be Rs. x and variable charge be Rs.y per km. Then,

x + 16y = 156 ...(i) and

x + 24y = 204 ...(ii)

Solving (i) and (ii), we get: x = 60, y = 6.

Therefore Cost of travelling 30 km = 60 + 30 y = Rs. (60 + 30 x 6) = Rs. 240.

Clearly, we have to first find two numbers whose difference is 2 and of which the smaller one is a perfect square and the bigger one a perfect cube.

Such numbers are 25 and 27.

Thus, Nitin is now 26 years old. Since the next perfect cube after 27 is 64,

so required time period = (64 - 26) years = 38 years.

Suppose the boy got x sums right and 2x sums wrong.

Then, x + 2x = 48 ⟺ 3x = 48 ⟺ x = 16.