Question

6) Two numbers are in the ratio 5:4. If they differ by 12, what are the numbers?​

Answer 1

$\textbf{Given:}$

$\textsf{Two numbers are in the ratio 5:4}$

$\textsf{and their difference is 12}$

$\textbf{To find:}$

$\textsf{The numbers}$

$\textbf{Solution:}$

$\textsf{Let the two numbers be x and y with}\;\mathsf{x\;>\;y}$

$\textsf{As per given data,}$

$\mathsf{x:y=5:4\;\;\&\;\;x-y=12}$

$\mathsf{Then,\;x=5k\;\;and\;\;y=4k}$

$\mathsf{x-y=12}$

$\implies\mathsf{5k-4k=12}$

$\implies\mathsf{k=12}$

$\mathsf{Now}$

$\mathsf{x=5k=5(12)=60}$

$\mathsf{y=4k=4(12)=48}$

$\textbf{Answer:}$

$\textsf{The two numbers are 60 and 48}$

Answer 2

SOLUTION

• Two numbers are in the ratio 5 : 4

• They differ by 12

TO DETERMINE

The numbers

EVALUATION

Here it is given that the numbers are in the ratio 5 : 4

Let the numbers are 5x and 4x

Now it is given that the numbers are differ by 12

So by the given condition

$\sf{5x - 4x = 12}$

$\sf{ \implies \: x = 12}$

So First number = 5 × 12 = 60

Second number = 4 × 12 = 48

FINAL ANSWER

The required numbers are 60 & 48

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