Rachael and Olivia are business partners in RO Dance. Their partnership agreement states that the partners will share income in a $3$:$2$ ratio $($Rachael; Olivia$).$ For the year ended December $31,2021,$ the partnership earned $$120,000.$ During $2021,$ Rachael withdrew $$20,000$ cash from the business and Olivial withdrew $$10,000$ cash. How much income would be allocated to Olivia?

a

$$52,000$

b

$$38,000$

c

$$50,000$

d

$$80,000$