**(1)**In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament ?

- 12
- 15
- 30
- 36

**Answer: Option B**

**Explanation:**

**I. matches of first player with other 5 players**

**II. matches of second player with 4 players other than the first player**

**III. matches of third player with 3 players other than the first player and second player.**

**IV. matches of fourth player with 2 players other than the first player, second player and third player.**

**V. matches of fifth player with 1 player other than the first player, second player, third player and fourth player.**

**So total matches will be 5+4+3+2+1 = 15**

**(3)**A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there ?

- 8
- 10
- 12
- 14

**Answer: Option D**

**Explanation:**

**Let number of horses = number of men = x.**

Then, number of legs = 4x + 2 x (x/2) = 5x.

So, 5X = 70 or x = 14.

Then, number of legs = 4x + 2 x (x/2) = 5x.

So, 5X = 70 or x = 14.

**(4)**A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?

- 9, 46
- 9, 50
- 10, 46
- 10, 50

**Answer: Option B**

**Explanation:**

**As from the question we have,**

A = 3B --- (i)

c - 4 = 2(A+4) ---(ii)

Also, A + 4 = 31

or A = 31-4 = 27

Putting A = 27 in (i) we get

B = 9

Putting A = 27 in (ii) we get

C = 50

A = 3B --- (i)

c - 4 = 2(A+4) ---(ii)

Also, A + 4 = 31

or A = 31-4 = 27

Putting A = 27 in (i) we get

B = 9

Putting A = 27 in (ii) we get

C = 50

**(5)**Reena is twice as old as Sunita. Three years ago, she was three times as old as Sunita. How old is Reena now ?

- 6 years
- 12 years
- 14 years
- 16 years

**Answer: Option B**

**Explanation:**

**Let Sunita's present age = x years**

Then Reena present age = 2x years

Three years ago

(2x-3) = 3(x-3)

2x - 3 = 3x - 9

or x = 6

Reena age = 2x = 2*6 = 12 year.

Then Reena present age = 2x years

Three years ago

(2x-3) = 3(x-3)

2x - 3 = 3x - 9

or x = 6

Reena age = 2x = 2*6 = 12 year.