The ratio of madhus age and karinas age is 6:7.after 12years the ratio of their ages will be 12:13. Find their present ages?

6/7 = m/k so m = 6 k/7

12/13 = (m+12)/(k+12)

or
12/13 = (6k/7 + 12) / (k+12)

12/13 = (6 k + 84)/7(k+12)

84 (k+12) = 13 (6 k + 84)

84 k + 1008 = 78 k + 1092

6 k = 84

k = 14
then m = 6 k/7 = 12

let their ages be 6x and 7x

(6x+12)/(7x+12) = 12/13
78x + 156 = 84x + 144
-6x = -12
x = 2

they are now 12 and 14

To find their present ages, let's assume Madhu's age is 6x and Karina's age is 7x.

According to the given ratio, after 12 years, Madhu's age will be 6x + 12 and Karina's age will be 7x + 12.

Given that the ratio of their ages after 12 years is 12:13, we can set up the equation:

(6x + 12) / (7x + 12) = 12/13

Cross-multiplying, we get:

13(6x + 12) = 12(7x + 12)

Simplifying the equation:

78x + 156 = 84x + 144

Subtracting 78x from both sides:

156 = 6x + 144

Subtracting 144 from both sides:

12 = 6x

Dividing both sides by 6:

x = 2

Now we can find Madhu's and Karina's present ages:

Madhu's age = 6x = 6(2) = 12 years
Karina's age = 7x = 7(2) = 14 years

Therefore, Madhu's present age is 12 years and Karina's present age is 14 years.