Two numbers are in the ratio of 5:6. If 8 is subtracted from each of the numbers the ratio becomes 4:5. find the numbers

Question

This question is based on the chapter linear equations in two variables. You have to find the numbers

Answer 1

 

X/Y = 5/6 ----> 6X = 5Y ---> y = (6/5)x

 

(x-8)/(y-8) = 4/5  ---->  5(x-8) = 4(y-8)

 

                                    5x - 40 = 4y - 32

 

                                     5x - 4y = -32 + 40

 

                                       5x - 4y = 8

 

 

                                     5x - 4(6/5)x = 8

 

                                      5x - (24/5)x = 8

 

                                      (25/5)x - (24/5)x = 8

 

                                           (1/5)x = 8

 

                                           x = 40

 

 

                                        y = (6/5)x = (6/5)(40) = 48

 

 

40/48 = 5/6

 

(40-8)/(48-8) = 32/40 = 4/5

 

40 and 48

Answer 2

Well, without really doing the math, you can see that we've gone down 1 part in each part of the ratio. One part must be 8, so...

 

5(8) = 40

6(8) = 48