Question

two number are in the ratio 5:6 if 8 is subtract from each of the number the ratio befomes 4:5 . find the numbers

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Answer 1

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

December 20, 2019avatar

Dhruma Mulmuley

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ANSWER

Let the two numbers be x and y.

As per condition 1, i.e., Two numbers are in the ratio 5:6.

The equation becomes,

y

x

=

6

5

∴6x−5y=0 ..........(1)

As per condition 2, If 8 is subtracted from each of the numbers the ratio is 4:5.

The equation becomes,

y−8

x−8

=

5

4

∴5x−4y=8 ...........(2)

Equation (1) can be written as x=

6

5y

Substituting x=

6

5y

in (2) we get,

y=48

Re substituting y=48 in (1) we get,

x=40

Hence Numbers are 40,48.

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Answer 2

Answer:

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