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The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.

$3 over 7$
$4 over 8$
$2 over 7$
$3 over 8$

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22.

If the number p is 5 more than q and the sum of the squares of p and q is 55, then the product of p and q is

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23.

The sum of the four number is 48. When 5 and 1 are added to the first two and 3 and 7 are subtracted from the 3rd and 4th, the numbers will be equal. The numbers are

6, 10, 14, 18
5, 11, 13, 19
9, 7, 15, 17
4, 12, 12, 20

24.
Sum of a fraction and thrice of its reciprocal is $73 over 20.$ What is the fraction?

$4 over 5$

$9 over 4$

$4 over 9$

$5 over 4$

$5 over 4$

Let the number be x.
According to the question,
$straight x space plus space 3 over straight x space equals space 73 over 20$
$rightwards double arrow space space space fraction numerator straight x squared space plus space 3 over denominator straight x end fraction space equals space 73 over 20 rightwards double arrow space space space 20 straight x squared space plus space 60 space equals space 73 straight x rightwards double arrow space space space 20 straight x squared space minus space 73 straight x space plus space 60 space equals space 0 rightwards double arrow space space space 4 straight x left parenthesis 5 straight x space minus 12 right parenthesis space minus space 5 left parenthesis 5 straight x minus 12 right parenthesis space equals space 0 rightwards double arrow space space space space left parenthesis 4 straight x minus 5 right parenthesis thin space left parenthesis 5 straight x minus 12 right parenthesis space equals space 0 rightwards double arrow space space space space space space straight x space equals space 5 over 4$