Problems on Numbers Solved problems and Answers

1.    The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is
Explanation:
Let the numbers be x and (22 - x).
Then, 5x = 6(22 - x)
     11x = 132
       x= 12.
So, the numbers are 12 and 10.

2. In a pair of fractions, fractions A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
Explanation:
A =2B ‹=› B= 1/2 A.
So, AB    = 2/25
‹=› 1/2A2= 2/25
‹=› A2= 4/25
A= 2/5.

3. The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.
Explanation:
Let the numbers be x and (184 - x). Then,
x / 3 - (184-x)/7 = 8 <=> 7

4. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Explanation:
Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3      x = 11.
Third integer = x + 4 = 15.

5. The sum of two number is 25 and their difference is 13. Find their product.
Explanation:
Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x + y)2 - (x- y)2
   = (25)2 - (13)2
   = (625 - 169)
   = 456
 xy = 114.