Question

The ratio of 2 numbers is 2:3. if two is subtracted from the first number and 8 from the second the ration becomes reciprocal of the original .find the numbers

Answer 1

Answer:

1st no is 8

2nd no is 12

Step-by-step explanation:

ratio of 2 no. =2:3

let the 2 nos. be 2x and 2x respectively

now it's given 2 is subtracted from 1st no=2x-2

Then,

it's said 8 is subtracted from 2nd no.=3x-8

so after subtracting the ratio becomes 3:2 (its reciprocal)

ATQ,

2x-2/3x-8=3/2

3 (3x-8)=2 (2x-2)

9x-24=4x-4

9x-4x=24-4

5x=20

x=20/5

x=4

Now the 1st no is 2x =2×4=8

And 2nd no is 3x=3×4=12

HOPE THIS WILL HELP YOU:)

Answer 2

AnswEr:-

❀ The numbers Are:-

• First number = 8.

• Second number = 12.

Explanation:-

Given:-

• Two numbers are in ratio 2:3.

• If 2 is subtracted from first number and 8 is subtracted from second number then the ratio becomes reciprocal of the original (3:2).

To Find:-

• The numbers.

So,

• Let the first number be 2x and second number 3x.

• When 2 is subtracted from 2x it would become 2x-2.

• When 8 is subtracted from 3x it would become 3x-8.

Therefore ATQ:-

If 2 is subtracted from first number and 8 is subtracted from second number then the ratio becomes reciprocal of the original.

$\\ \tt\mapsto2x - 2 \ratio3x - 8 = 3 \ratio2. \\ \\ \tt\mapsto \frac{2x - 3}{3x - 8} = \frac{3}{2} . \\ \\ \tt\mapsto2(2x - 2) = 3(3x - 8). \\ \\ \tt\mapsto4x - 4 = 9x - 24. \\ \\ \tt\mapsto - 4 + 24 = 9x - 4x. \\ \\ \tt\mapsto20 = 5x. \\ \\ \tt\mapsto5x = 20. \\ \\ \tt\mapsto x = \cancel \frac{20}{5} . \\ \\ \tt\mapsto{ \underline{ \underline{ \: x = 4.}}}$

So the value of x is 4.

Therefore The Numbers are:-

$\\ \boxed{\tt\underline{\bigstar \: \: 2x = 2 \times 4 = 8.}} \\ \\ \rm and \\ \\ \boxed{\tt \underline {\bigstar \: \: 3x = 3 \times 4 = 12.}}$