The ages of Aryan and Rajiv are in the ratio 6:8. Three years from now, the ratio of their ages will be 4:5. Find the present ages of them.

:

The ratio of Aryan and Rajiv ages = 6:8

Then, age of

Aryan = \$6x\$, Rajiv = \$8x\$ → (1)

Three years from now, age of

Aryan = \$6x + 3\$, Rajiv = \$8x + 3\$

\$(6x + 3) : (8x + 3) = 4 : 5\$

⇒ \$5(6x + 3) = 4(8x + 3)\$

⇒ \$30x + 15 = 32x + 12\$

⇒ \$32x - 30x = 15 - 12\$

⇒ \$2x = 3\$

⇒ \$x = 3/2\$

Substitute '\$x = 3/2\$' in equation (1),

Aryan = \$\cancel6^3(3/\cancel2^1)\$, Rajiv = \$\cancel8^4(3/\cancel2^1)\$

⇒Aryan = \$3 \times 3\$, Rajiv = \$4 \times 3)\$

⇒Aryan = \$9\$, Rajiv = \$12\$

Therefore, the present ages of them are \$9\$, Rajiv = \$12\$.