**Question 1 :**

The sum of a number and its reciprocal is 65/8. Find the number.

**Question 2 : **

The difference of the squares of two positive numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

**Question 3 :**

A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences the sides of the rectangular garden letting his house compound wall act s the fourth side fence. Find the dimension of the garden.

**Question 4 :**

A rectangular field is 20 m long and 14 m wide. There is the path of equal width all around it having an area of 111 sq.m. Find the width of the path on the outside.

**Question 5 :**

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

**Question 6 :**

The speed of a boat in still water is 15 km/hr. It goes 3 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.

**Question 7 :**

One year ago a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present age.

**Question 8 :**

A chess board contains 64 equal squares and the area of each square is 6.25 cm^{2}. A border around the board is 2 cm wide. Find the length of the side of chess board.

**Question 9 :**

A takes less than the time taken by B to finish the piece of work. If both A and B together can finish the work in 4 days. Find the time that B would take to finish the work by himself.

**Question 10 :**

Two trains leave railway stations at the same time. The first train travels due west and the second train due north. The first travels 5 km/hr faster than the second train. If after two hours, they are 50 km apart, find the average speed of each train.

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