Question

alice and bob can complete a work in 4 days together. if alice alone can complete the same work in 12 days , how many days can bob alone complete the work?

a) 4
b) 5
c) 6
d) 7

Answer 1

Answer:

c)7 days ,, pls mark me as brainliest if you are satisfied

Step-by-step explanation:

A= Alice

b=Bob

if A completes the work in 12 days, then in one day the work done is 1/12th of the total work. Let the total work be 1.

Similarly for A and B to complete 1 work, they would take 4 days and in one day, 1/4th of total work is done by both of them.

So in one day A does 1/12th of the work and B does 1/B th of the work and together they complete 1/4th of the work.

Hence, 1/B + 1/12 = 1/4

Hence B =6.

Effectively B takes 6 days to complete the work.

Answer 2

Given :- Alice and bob can complete a work in 4 days together. if alice alone can complete the same work in 12 days , how many days can bob alone complete the work?

a) 4

b) 5

c) 6

d) 7

Solution :-

LCM of 4 and 12 = 12 units = Let total work .

so,

→ Efficiency of (Alice + bob) = (Total work) / (Total days) = (12/4) = 3 units/day .

and,

→ Efficiency of Alice = (Total work) / (Total days) = 12/12 = 1 unit / day.

then,

→ Efficiency of bob = Efficiency of (Alice + bob) - Efficiency of Alice = 3 - 1 = 2 units/day.

therefore,

→ Time taken by bob alone = (Total work) / Efficiency = 12/2 = 6 days. (C) (Ans.)

Hence, Bob alone can complete the work in 6 days.

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