7 CHAP

# 7 CHAP - 7 PROBLEMS ON NUMBERS In this section questions...

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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 one-third of the one exceeds one-seventh 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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7 CHAP - 7 PROBLEMS ON NUMBERS In this section questions...

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