Question

two numbers are in ratio 3:4 . If 2 is subtracted from the first number and 5 is subtracted from the second number , the ratio becomes the reciprocal of the original ratio . Find the number​

Answer 1

$\textbf{Given:}$

$\textsf{Ratio of two numbers is 3:4 and}$

$\textsf{2 is subtracted from the first number and 5 is subtracted}$

$\textsf{from the second number , the ratio becomes the reciprocal}$

$\textsf{of the original ratio}$

$\textbf{To find:}$

$\textsf{The numbers}$

$\textbf{Solution:}$

$\textsf{Let the given two numbers be x andy}$

$\textsf{As per given data,}$

$\mathsf{x:y=3:4}$

$\mathsf{Then,\;x=3k,\;y=4k}$

$\mathsf{Also,}$

$\mathsf{x-2:y-5=4:3}$

$\mathsf{\dfrac{x-2}{y-5}=\dfrac{4}{3}}$

$\mathsf{\dfrac{3k-2}{4k-5}=\dfrac{4}{3}}$

$\mathsf{3(3k-2)=4(4k-5)}$

$\mathsf{9k-6=16k-20}$

$\mathsf{7k=14}$

$\mathsf{k=2}$

$\mathsf{Now,}$

$\mathsf{x=3k=3(2)=6}$

$\mathsf{y=4k=4(2)=8}$

$\therefore\textsf{The required numbers are 6 and 8}$

Answer 2

Answer:

let the given two numbers B X and Y

Step-by-step explanation:

as per given data

x:y= 3:4

then ,x= 3 k,y=4k

Also x-2:y-5=4:3

3k-2 =4, 4k-5 =3

3(3k-2)=4(4k-5)

9k-6 16 k - 20

7k=14

K =2

Now = X=3k=3 (2)=6

y=4k=4(2)=8

Ans= the required numbers are 6 and 8

this is the answer