7. 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
.
(Hotel Management, 2002)
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.
(S.S.C. 2000)
Sol.
Let the number be x.
Then, x + (1/x) = 13/6 => (x
2
+ 1)/x = 13/6 => 6x
2
– 13x + 6 = 0
=> 6x
2
– 9x – 4x + 6 = 0 => (3x – 2) (2x – 3) = 0
x = 2/3 or x = 3/2
Hence the required number is 2/3 or 3/2.
Ex. 4. The sum of two numbers is 184. If onethird of the one exceeds oneseventh
of the other by 8, find the smaller number.
Sol.
Let the numbers be x and (184 
x).
Then,
(X/3)  ((184 – x)/7) = 8 => 7x – 3(184 – x) = 168 => 10x = 720 => x = 72.
So, the numbers are 72 and 112. Hence, smaller number = 72.
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 Spring '11
 vinh
 Numerical digit, Decimal, Sol.

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