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 p. 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 p.

Answer:

Let the three positive integers be

Given

Therefore the numbers are

Question 15: A can do a piece of work in ‘x’ days and B can do the same work in (x+16) days. If both working together can do it in 15 days: calculate ‘x’.

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 x 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