**Problem 1 :**

Find two consecutive positive even integers whose squares have the sum 340.

**Problem 2 :**

The sum of two squares of three consecutive natural numbers is 194. Determine the numbers.

**Problem 3 :**

The product of two successive multiples of 3 is 810. Find the multiples.

**Problem 4 :**

The sum of the squares of two natural numbers is 34 and sum of 5 times the smaller and 3 times the larger is 30. Find the numbers.

**Problem 5 :**

Two natural numbers differ by 2 and their product is 360. Find the numbers.

**Problem 6 :**

There are three consecutive positive integers such that the sum of the square of first and the product of the other two is 154. Find the integers.

**Problem 7 :**

Find two consecutive natural numbers whose product is 30.

**Problem 8 :**

The sum of two numbers is 60 and their product is 576. Find the numbers.

**Problem 9 :**

Two positive numbers differ by 4 and their product is 192. Find the numbers.

**Problem 10 :**

The sum of the number and its positive square root is 7/36. Find the number.

**Problem 11 :**

The sum of two numbers is 15 and the sum of its reciprocals is 3/10. Find the numbers.

**Problem 12 :**

The sum of two numbers is 60 and their product is 576. Find the numbers.

**Problem 13 :**

Two positive numbers differ by 4 and their product is 192. Find the numbers.

**Problem 14 :**

A two digit number is four times the sum of its digits and twice the product of the digits. Find the number.

**Problem 15 :**

A two digit number such that the product of its digits is 21. When 36 is subtracted from the number the digits are interchanged. Find the number.

**Problem 16 :**

A two digit number is such that the product of its digits is 12. When 36 is added to this number the digits are interchanged. Find the numbers.

**Problem 17 :**

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.

**Problem 18 :**

The denominator of the fraction is 5 more than its numerator. The sum of the fraction and its reciprocal is 73/24. Find the fraction.

**Problem 19 :**

The denominator of the fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58/21, find the fraction.

**Problem 20 :**

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 1. In case, the numerator is decreased by 4 and the denominator by 2, it becomes 1/2. Find the fraction.

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