Question

Two numbers are in the ratio 2:3 and if 5 is subtracted from each, they
are reduced to the ratio 3:5. The smaller number is​

Answer 1

Answer:

Smaller number = 33

Bigger number = 55

Step-by-step explanation:

Let the numbers in the ratio 3 : 5 be 3x and 5x

If 9 subtracted from each of them, the numbers becomes 3x - 9 and 5x - 9

When 9 subtracted from 3x and 5x, the ratio of the numbers becomes 12 : 23.

According to the question,

=  

23(3x - 9) = 12(5x - 9)

69x - 207 = 60x - 108

69x - 60x = 207 - 108

9x = 99

x =  

x = 11

1st number => 3x

=> 3 * 11

=> 33

2nd number => 5x

=> 5 * 11

=> 55

∴ The smaller number is 33 and the bigger number is 55 respectively.

Answer 2

Answer:

The numbers are $20,30$.

Step-by-step explanation:

Ratio represents how many times one number contains another.

It generalized the number.

It is given that two numbers are in the ratio $2:3$.

If $5$ is subtracted from each, they are reduced to the ratio $3:5$.

We need to find the smaller number.

As per the definition of the ratio studied above,

Let smaller number be $2x$

Let larger number be $3x$.

As per the question

$\frac{2x-5}{3x-5} =\frac{3}{5}$

Solving

$10x-25=9x-15$

$x=10$

Smaller number $=2x=2(10)=20$

Larger number $=3x=3(10)=30$

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