Question : When simplified, the product $(2- \frac{1}{3}) (2-\frac{3}{5}) (2- \frac{5}{7}) .... (2- \frac{997}{999})$ equals:

Option 1: $\frac{5}{999}$

Option 2: $\frac{5}{3}$

Option 3: $\frac{1001}{999}$

Option 4: $\frac{1001}{3}$

Question : What is the value of $999 \frac{1}{2} + 999 \frac{1}{6} + 999\frac{1}{12}+999 \frac{1}{20} + 999\frac{1}{30}?$

Option 1: $999\frac{1}6$

Option 2: $999\frac{5}6$

Option 3: $4995\frac{1}6$

Option 4: $4995\frac{5}6$

Question : The ratio of two numbers is 4 : 5. If both numbers are increased by 4 the ratio becomes 5 : 6. What is the sum of the two numbers?

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 36

Question : The ratio of two numbers is 3 : 5. If both numbers are increased by 8, the ratio becomes 13 : 19. What is the sum of the two numbers?

Option 1: 32

Option 2: 48

Option 3: 40

Option 4: 72

Question : If the square of the sum of two numbers is equal to 4 times their product, then the ratio of these numbers is:

Option 1: 2 : 1

Option 2: 1 : 3

Option 3: 1 : 1

Option 4: 1 : 2