Question 1: The product of two consecutive integer is 56. Find the integers.

Answer:

Let the two consecutive integers be

Therefore

Therefore the two integers could be

Question 2: The sum of the square of two consecutive natural numbers is 41. Find the numbers.

Answer:

Let the two consecutive integers be

or

or

or

Therefore the two integers could be

Question 3: Find the two natural numbers which differ by 5 and the sum of square is 97.

Answer:

Let the two numbers be

or

or

Therefore

Therefore the two natural numbers could be

Question 4: The sum of a number and its reciprocal is 4.25. find the number.

Answer:

Let the numbers be

or

or

Let the numbers will be

Question 5: Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is 7/10.

Answer:

Let the two natural numbers be

Therefore the two natural numbers are

Question 6: Divide 15 into two parts such that the sum of reciprocal is 3/10.

Answer:

Let the two parts be

Therefore the two parts should be

Question 7: The sum of the square of two positive integer is 208. If the square of the larger number is 18 times the smaller number, find the numbers.

Answer:

Let the two numbers be

given

and

Therefore

or

Therefore

Question 8: The sum of the square of two consecutive positive even numbers is 52. Find the numbers.

Answer:

Let the two consecutive numbers be

therefore

Therefore the two numbers are

Question 9: Find two consecutive positive odd numbers. The sum of whose square is 74.

Answer:

Let the two consecutive numbers be

Therefore

Therefore the two numbers are

Question 10: The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.

Answer:

let the fraction be

Therefore the fraction is

Question 11: Three positive numbers are in the ratio . find the numbers if the sum of their squares is 244.

Answer:

Let the fractions be

Given

or

Therefore the numbers are

Question 12: Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

Answer:

Let the two parts be

Given

Therefore the two parts are

Question 13: Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60.

Answer:

Let the three consecutive number be

Given

Therefore the numbers are

Question 14: Out of three consecutive positive integers, the middle number is . if three times the square of the larger is greater than the sum of the squares of the other two numbers by 67; calculate the value of .

Answer:

Let the three positive integers be

Given

Therefore the numbers are

Question 15: A can do a piece of work in days and B can do the same work in days. If both working together can do it in 15 days: calculate .

Answer:

Given

Question 16: One pipe can fill a cistern in 3 hours less than the other. Two pipes together can fill cistern in 6 hours and 40 minutes. Find the time that each pipe will take to fill the cistern.

Answer:

Given

(ignore this as it is not possible)

Therefore the time taken by the first pipe to fill in the cistern is hours and the second one hours.

Question 17: A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking as the smaller part of the two parts, find the number. [2010]

Answer:

Let the two parts be

Given

Also

Substituting it back

(ignore this as the number is positive)

Therefore the larger part is

Hence the number is