Two numbers are in the ratio 7:5 . When 10 is subtracted from each term , the ratio becomes 3:2 .Find the numbers.

Denote the two numbers: a and b

Two numbers are in the ratio 7:5

=> a/b = 7/5

=> a = (7/5) x b     (1)

When 10 is subtracted from each term , the ratio becomes 3:2

=> (a - 10)/(b - 10) = 3/2

=> 2 x (a - 10) = 3 x ( b - 10)

=> 3 x b - 2 x a = 10

From (1) => 3 x b - 2 x (7/5) x b = 10

             => (1/5) x b = 10

             => b = 50

             => a = (7/5) x b = (7/5) x 50 = 70

Hope this helps!

:)

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