Question

the ages of anu and manu are in the ratio 5 is to 6 four years ago their ages where in the ratio 3 is to 4 find their present ages​

Answer 1

Let the rational between ages of Anu and Raj be x

Present ages of Anu and Raj are in the ratio 4:5. So their ages are 4x and 5x

Eight years from now the ratio of their ages will be 5:6

8 years from now their ages, 4x + 8 and 5x + 8

Their ratio is 5 : 6

4x + 8/5x + 8 = 5/6

Cross multiplication

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

25x + 40 = 24x + 48

25x - 24x = 48 - 40

x = 8

The rational is 8, their ages

Anu’s present age 4x = 4 × 8 = 32 years

Raj's present age 5x = 5 × 8 = 40 years

Answer the present ages of Anu is 32 years and present age of Raj is 40 years.

Answer 2

Answer:

$let \: the \: present \: age \: of \: anu \: be \: 5x \\ \\ present \: age \: of \: manu \: is \: 6x \\ \\ before \: 6 \: years \\ \\ anu \: age \: was = 5x - 6 \: years \\ \\ manu \: present \: was = 6x - 6 \: years \\ \\ acq \\ \\ \frac{5x - 6}{6x - 6} = \frac{3}{4} \\ \\ 4(5x - 6) = 3(6x - 6) \\ \\ 20x - 24 = 18x - 18 \\ \\ 20x - 18x = - 18 + 24 \\ \\ 2x = 6 \\ \\ x = 3 \\ \\ anu \: age = 5 \times 3 = 15 \: years \\ \\ manu \: age = 6 \times 3 = 18years$