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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

10

-10

15

-15

According to the question,
p - q = 5 ...(i)
p² + q² = 55 ...(ii)
Squaring both the sides in Eq. (i), we get
(p - q)² = (5)² ⟹ p² + q² - 2pq = 25
⟹ 55 - 2pq = 25
⟹ - 2pq = -30
⟹ pq = 15

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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