Question

The ratio of two numbers is 5:4 and if 10 is added to each number, then the ratio becomes 6:5. The
numbers will be :
​

Answer 1

Answer:

50 and 40

Step-by-step explanation:

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Answer 2

Two numbers are 50 and 40

Given :

• Two numbers are in the ratio 5 : 4

• When 10 is added to each number, then the ratio becomes 6 : 5.

To find :

The numbers

Solution :

Step 1 of 2 :

Form the equation to find the numbers

Two numbers are in the ratio 5 : 4

Let the numbers are 5x and 4x

Now it is given that when 10 is added to each number, then the ratio becomes 6 : 5.

By the given condition

$\displaystyle \sf{ (5x + 10):(4x + 10) = 6 : 5 }$

Step 2 of 2 :

Find the numbers

$\displaystyle \sf{ (5x + 10):(4x + 10) = 6 : 5 }$

$\displaystyle \sf{ \implies \frac{5x + 10}{4x + 10} = \frac{6}{5} }$

$\displaystyle \sf{ \implies 25x + 50 = 25x + 60 }$

$\displaystyle \sf{ \implies 25x - 24x = 60 - 50 }$

$\displaystyle \sf{ \implies x = 10}$

First number = 5x = 5 × 10 = 50

Second number = 4x = 4 × 10 = 40

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