Solution:

Let the cost of cap = m
Cost of pen = (5 + m)

As per the condition

5.50 = 5 + m + m
2m = 0.5
m = 0.25

Hence, the cap costs 25 Paise.

Solution:

28 is the required number.

28 * 3 - 2 = 82.

Solution:

16

Explanation:
Let the number be p, then the square will be p^2
According to question:
2p = (p/4) + 7
=> 8p = p + 28
=> p = 4

p^2 = 4^2 = 16.

Solution:

80,000.

Explanation:
The distance traveled by each tyre:
4/5 * 1, 00, 000km = 80,000 km.

Solution:

She has misplaced 119 pens in total.

Solution:

60 minutes

Explanation:
Roy will be able to consume all the five tablets in an hour.

Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.

Solution:

father:72, Son:27

Explanation:
The only single digit prime numbers are 2, 3, 5 and 7.
Let us use the possible combinations and check when the difference comes to be 45.
Son = 23, Father = 32, Difference = 7
Son = 25, Father = 52, Difference = 27
Son = 27, Father = 72, Difference = 45

This stand apt for the requirements. Thus the present age of the father is 72 years and that of son is 27 years.

Solution:

The required number is 499449.

The maximum sum of a number under 5 lakh will be of the number 499999 i.e. 49.
Thus the required number must be close to 499999.
The root of 499999 ~ 707.106
By calculating the square of 707, we get 499849 which is the answer.

Solution:

19

Explanation:
77 empty bottles = 15 full bottles + 2 empty bottles
15 full bottles will give him 15 empty bottles more.
15 + 2 = 17
17 empty bottles = 3 full bottles + 2 empty bottles
3 full bottles will give him 2 empty bottles more.
3 + 2 = 5
5 empty bottles = 1 filled bottle

15 + 3 + 1 = 19

Thus we will be able to get 19 full bottles of soft drink.

Solution:

Box A has five balls and Box B has seven balls.