Question

Alice and Bob share an allotment. The ratio of the area of Alice's

portion to the area of Bob's portion is 3:2. They each grow
vegetables and fruit on the allotment. The entire allotment is
covered by vegetables and fruit in the ratio 7:3. On Alice's
portion of the allotment, the ratio of vegetables to fruit is 4:1
What is the ratio of vegetables to fruit in Bob's portion?​

Answer 1

11:39

Explanation:

Bob's portion of the allotment :

`Total\:ratio=3+2 =5\\\\= (2)/(5)`

Alice's portion :

`Total\:ratio=3+2 =5\\\\= (3)/(5)`

Vegetables are :

`Total\:ratio=7+3 =10\\\\= (7)/(10)` of the total area

Vegetables are :

`Total\:ratio=4+1 =5\\\\= (4)/(5)` of Alice's portion, or:

`(4)/(5) *((3)/(5) ) = (12)/(25)`

Bob's portion fraction (b):

`(12)/(25) + b = (7)/(10)`

L.C.M of 25 and 10 =50

`(24)/(50) + b = (35)/(50) \\\\b =(11)/(50)\\\\ Ratio:\\50 - 11 = 39`

Bob's vegetable to fruit ratio is 11 : 39