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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