21 Two numbers are in the ratio of 5 6. If 7 is subtracted from each of the numbers, the ratio becomes 4 5. Find the numbers.

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Solution

Dear student,

$L e t t h e n u m b e r s b e 5 x a n d 6 x, w h e n 7 i s s u b t r a c t e d f r o m b o t h r a t i o b e c o m e s 4 : 5 i . e \frac{(5 x - 7)}{(6 x - 7)} = \frac{4}{5} 5 \times (5 x - 7) = 4 \times (6 x - 7) 25 x - 35 = 24 x - 28 25 x - 24 x = 35 - 28 x = 7 \Rightarrow 5 x = 35 a n d 6 x = 42 t h e r e f o r e t h e n u m b e r s a r e 35 a n d 42$

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