Question 1: The product of two consecutive integer is 56. Find the integers.
Answer:
Therefore the two integers could be
Question 2: The sum of the square of two consecutive natural numbers is 41. Find the numbers.
Answer:
Therefore the two integers could be
Question 3: Find the two natural numbers which differ by 5 and the sum of the square is 97.
Answer:
Let the two numbers be
Therefore the two natural numbers could be
Question 4: The sum of a number and its reciprocal is 4.25. find the number.
Answer:
Question 5: Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is 7/10.
Answer:
Therefore the two natural numbers are
Question 6: Divide 15 into two parts such that the sum of reciprocal is 3/10.
Answer:
Therefore the two parts should be
Question 7: The sum of the square of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers.
Answer:
Let the two numbers be
and
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 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 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:
Question 11: Three positive numbers are in the ratio . find the numbers if the sum of their squares is 244.
Answer:
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:
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
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
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:
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:
(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:
Substituting it back
(ignore this as the number is positive)
Therefore the larger part is
Hence the number is