Question

Two numbers are in the ratio 5 : 6. When 2 is added to first and 3 is added to
second, they are in the ratio 4: 5. Find the numbers.
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Answer 1

Step-by-step explanation:

let the numbers be 5x and 6x

a/q

5x+2/6x+3=4/5

5(5x+2)=4(6x+3)

25x+10=24x+12

25x-24x=12-10

x=2

then first number= 5*2=10

and second number=6*2=12

Answer 2

Step-by-step explanation:

Given -

Two numbers are in ratio 5 : 6

When 2 added to first number and 3 to second the ratio become 4 : 5

To find -

the numbers

Solution -

Let us think the numbers as 5x and 6x

First number + 2 = 5x + 2

Second number + 3 = 6x + 3

Real ratio = 4 : 5

so,

5x + 2 : 6x + 3 = 4 : 5

$\frac{5x + 2}{6x + 3} = \frac{4}{5} \\ (after \: cross \: multiplication) \\ = > 5 \times (5x + 2) = 4 \times (6x + 3) \\ = > 25x + 10 = 24x + 12 \\ = > 25x = 24x + 12 - 10 \\ = > 25x - 24x = 12 - 10 \\ = > x = 2$

First number = 5x = 5(2) = 10

Second number = 6(2) = 12

The numbers are in ratio 5 : 6. after adding 2 to first and 3 to second the ratio will be 4 : 5.

Hence we have found the correct numbers.

hope it helps.