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.

Operator used : Ratio

:

The ratio of Aryan and Rajiv ages

6:8

Then, age of

Aryan = \$6x\$
Rajiv = \$8x\$

Three years from now, age of

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

On Simplification

\$(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\$

On Cancellation

Substitute '\$x = 3/2\$'

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 Aryan and Rajiv are

\$9\$ and \$12\$.