Question

011. Find two numbers in the ratio 8:7 such that when each is decreased by 12, they are in the ratio
11:9.
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Answer 1

Answer:

11:9

Step-by-step explanation:

Ratio = 8:7

Consider the numbers as 8x and 7x

They are decreased by 12  

2

1

​  

=  

2

25

​  

 

Sp, using the condition

[7x–  

2

25

​  

]

[8x–  

2

25

​  

]

​  

=  

9

11

​  

 

Taking LCM

[  

2

(14x–25)

​  

]

[  

2

(16x–25)

​  

]

​  

=  

9

11

​  

 

By further calculation

(14x–25)

(16x–25)

​  

=  

9

11

​  

 

By cross multiplication

154x–275=144x–225

154x–144x=275–225

10x=50

x=  

10

50

​  

=5

So the numbers are

8x=8×5=40

7x=7×5=35