Arithmatical - Problems On Numbers

DIRECTIONS : Problems based on Numbers.
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
  A.  10
  B.  12
  C.  15
  D.  16
Solution
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. If the sum and the difference of two numbers are 20 and 8 respectively, then the difference of their square is
  A.  12
  B.  28
  C.  160
  D.  180
Solution
Let the numbers be x and y.
Then, x + y = 20 and x - y = 8.
Therefore,x2 - y2 = (x + y)(x - y)
‹=› 20 x 8
‹=› 160.

3. Let the number which when multiplied by 15 is increased by 196.
  A.  14
  B.  20
  C.  26
  D.  28
Solution
Let the number be x .
Then, 15x - x = 196
‹=›14x = 196
x ‹=› 14.
4. The sum of two numbers is 25 and their difference is 13. Find their product.
  A.  104
  B.  114
  C.  315
  D.  325
Solution
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.
5. Three numbers are in the ratio of 3 : 4 : 6 and their product is 1944. The largest of these numbers is
  A.  6
  B.  12
  C.  18
  D.  26
Solution
Let the numbers be 3x, 4x and 6x.
Then, 3x × 4x × 6x = 1944
‹=›72x3 = 1944
‹=›x3 = 27
‹=›x = 3
Therefore, Largest number = 6x = 18.
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