Problem Solving

Elizabeth and Scott each recieve a share of lottery prize that is paid in 12 equal installments on the last day of each month for 20 years. If the amount paid to Elizabeth in the first three months of a year is equal to the amount paid to Scott in the first nine months of a year, what is the ratio of dollar value of Scott's prize to dollar value of Elizabeth's prize.

1. 1:3

2. 7:11

3. 2:3

4. 9:13

5. 3:4

Answer is (A) i.e. 1/3

Let Elizabeth & Scott get X per month in total
Let Elizabeth get E per month
Let Scott get X-E per month

According to Question,

3E=9(X-E)
E = 3/4 * X

X-E=X/4

Scott/Elizabeth = 1/3

IMO A


take monthly share of elisabeth = E
monthly share of Scott = S

given 3E = 9S

S/E = 3/9 hence A