A book needs to be typed. When working alone. A types it in 15 days. B types it in 12 days. C types it in 20 days. and D types it in 8 days, If A and D work together as team SUN. B and C work as team MOON. and A and C work as team RED. Which team finishes typing the book in the least time?

Correct option is B

Given:

A's time to type the book = 15 days 

B's time to type the book = 12 days

C's time to type the book = 20 days

D's time to type the book = 8 days

Solution:

Individual work rates:

A's work rate = $$\frac{1}{15}$$ books/day

​B's work rate = $$\frac{1}{12}$$ books/day

​​C's work rate $$\frac{1}{20}$$  books/day

​D's work rate $$\frac{1}{8}$$books/day

Combined work rates for each team:

​Team SUN (A and D):

​Combined work rate = $$\frac{1}{15}+\frac{1}{8}$$ = $$\frac{8+15}{120}$$ = $$\frac{23}{120}$$ 

Time taken = $$\frac{120}{23}$$ = 5.22 days

​Team MOON (B and C):

​Combined work rate = $$\frac{1}{12}+\frac{1}{20}$$ = $$\frac{5+3}{60}$$ = $$\frac{8}{60}$$ = $$\frac{4}{30}$$

​​Time taken = $$\frac{30}{4}$$ = 7.5 days

​Team RED (A and C):

​Combined work rate =  $$\frac{1}{15}+\frac{1}{20}$$ = $$\frac{4+3}{60}$$= $$\frac{7}{60}$$

​​Time taken = $$\frac{60}{7}$$ = 8.57

​Team SUN (A and D): Approximately 5.22 days

Team MOON (B and C): 7.5 days

Team RED (A and C): Approximately 8.57 days

The team that finishes typing the book in the least time is Team SUN

Thus, correct answer is (b)  Team Sun

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