Question

ratio of two numbers is 3:5.if 4 is subtracted form each number then the ratio becomes 5:9.find the numbers​

Answer 1

Here is your Answer with step-by-step explanation:-

Method 1: Equations

Let the numbers be  3x  and  4x . When 4 is subtracted from both, we get

(3x−4):(4x−4)::5:7  

21x−28=20x−20  

x=8  

So the numbers are 24 and 32.

Method 2: Observation

Observe the two ratios  3:4  and  5:7 .

The difference between 3 and 4 is 1 while the difference between 5 and 7 is 2.

When we subtract a constant from both the terms, the difference between them will not change. As a first step, let us ensure that the difference is the same in both the ratios. It is easy to increase the difference in the first ratio to 2. We just need to double both the terms in the ratio. Let us express  3:4  as  6:8.  We now have two ratios  6:8  and  5:7 .

6:8  becomes  5:7  when we subtract 1 from both the terms. We want to retain the same relationship when we subtract 4 from both the terms. This can be accomplished if we start with numbers which are 4 times these.

The ratio  6:8  can be written as  24:32  while  5:7  can be written as  20:28 .

The original numbers are 24 and 32 (which are clearly in the ratio  3:4 ). After subtracting 4 from each, we get 20 and 28 which are in the ratio  5:7 .

Note: I have written two methods, you can copy any method.

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Answer 2

Answer:

Let the number be x and y then x:y =3:5

x/y = 3/5 = 5x = 3y = x = 3y/5

according to the question

x-4/y-4 = 5/9

solving this equation

9(x-4) = 5(y-4)

9x-36 = 5y-20

9x-5y = 36-20

9x-5y = 16

substituting equation i and ii

9(3y/5) = 5y = 16

27y/5 = 5y = 16

27y-25y = 80

2y = 80

y= 80/2

y= 40

Now x = 3y/5 = 3×40/5 = 24

Hence the number and fraction = (24,40)

and 24/40 respectively

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