Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

Manick's present age = 12 years, Rahul's present age = 4 years.

Let Manick be twice as old as Rahul after x years from now.

Then, 12 + x = 2 (4 + x) ⟺ 12 + x = 8 + 2x ⟺ x = 4.

Hence, Manick's required age = 12 + x = 16 years.

'All but nine died' means 'All except nine died' i.e. 9 sheep remained alive.

Let number of notes of each denomination be x.

Then, x + 5x + 10x = 480 ⟺ 16x = 480 ⟺ x = 30.

Hence, total number of notes = 3x = 90.

Let money with Ken = x. Then, money with Mac = x + £ 3.

Now, 3x = (x + x + £ 3) + £ 2 ⟺ x = £ 5.

Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.

Ayush's present age = 10 years.

His mother's present age = (10 + 20) years = 30 years.

Ayush's father's present age = (30 + 5) years = 35 years.

Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.

Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.

Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.

So, required number = 10 + 10 = 20.