Question

(b) Two numbers are in the ratio 4:5. If 6 and 5 are added to the first and second numbers
respectively, the ratio become 5:6. Find the numbers.
8​

Answer 1

Answer:

let the two numbers are 4x and 5x

then

after adding 6 to the first number and 8 to the second number the ratio = 11:14

4x+6/(5x+8) = 11:14

14(4x+6)=11(5x+8)

56x+84=55x+88

56x-55x =88-84

x=4

there fore required numers are

first = 4x = 4×4 =16

second = 5x =5×4=20

Step-by-step explanation:

plz ark brilliantest

Answer 2

Answer:

$\large\tt\color{red}\underline{\underline{Question:}}$

$\textsf{Two numbers are in the ratio 4:5 . If 6 and 5 are}$

$\textsf{added to the first and second numbers}$

$\textsf{respectively,the ratio become 5:6.Find}$

$\textsf{the numbers.}$

$\large\tt\color{blue}\underline{\underline{Given:}}$

$\textsf{Ratio before added = 4:5}$

$\textsf{Ratio after added = 5:6}$

$\textsf{Numbers added = 6 and 5}$

$\large\tt\color{pink}\underline{\underline{To\:find:}}$

$\textsf{Numbers which are in ratio 4:5}$

$\large\tt\color{purple}\underline{\underline{Taken:}}$

$\textsf{Let the numbers be x}$

$\textsf{(6 is added with 4x . So , it will be)}$

$\Rightarrow{4x+6}$

$\textsf{(5 is added with 5x . So , it will be)}$

$\Rightarrow{5x+5}$

$\textsf{So,the full equation will like this}$

$\Rightarrow{(4x+6)/(5x+5)=5:6}$

$\large\tt\color{green}\underline{\underline{Solution:}}$

$\rightarrow{(4x+6)/(5x+5)=5:6}$

$\rightarrow{6(4x+6)=5(5x+5)}$

$\rightarrow{24x+36=25x+25}$

$\rightarrow{36-25=25x-24x}$

$\rightarrow{11=x}$

$\therefore\boxed{1st\:number=4×11=44}$

$\therefore\boxed{2nd\:number=5×11=55}$

$\large\tt\color{purple}\underline{\underline{Verification:}}$

$\textsf{To verify divide the numbers and divide after adding also}$

$\textsf{First before adding if the ratio come same then}$

$\textsf{the answer will correct}$

$\mapsto{Ratio=\frac{44}{55}}$

$\mapsto{Ratio=4:5}$

______________________________

$\textsf{Now divide after adding}$

$\mapsto{Ratio=\frac{44+6}{55+5}}$

$\mapsto{Ratio=\frac{50}{60}}$

$\mapsto{Ratio=5:6}$

..................................................................

So, the answers come same 4:5 and 5:6 .

Hence , the answer is also verified .