. PROBLEMS ON NUMBERS
In this section, questions involving a set of numbers are
put in the form of a puzzle. You have to analyze the given conditions, assume
the unknown numbers and form equations accordingly, which on solving yield the
unknown numbers.
Solved examples.
Ex. 1. A number is as much greater than 36 as is less than
86.find the number.
Sol. let the number be x. then, x -36 = 86 –X 2X =86 + 36 = 122 x = 61.
Hence, the required number is 61.
Ex.2. find a number such that when 15 is subtracted from 7
times the number, the result is 10 more than twice the number.
Sol. let the number be x. then, 7X -15=2X + 10 5X =25
x=5.
Hence, the required number is 5.
Ex.3. the sum of a rational number and its reciprocal is
13/6. Find the number.
Sol. let the number be x.
Then, x + 1/X = 13/6
X²
+ 1 / x = 13/6 6x² - 13X + 6 =0
6X² - 9X -4X + 6 = 0 (3X –
2) (2X -3) =0.
X = 2/3 or X = 3/2
Hence, the required the number is 2/3 or 3/2
Ex. 4. 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.
