Question

A and b took a job to be completed in 20 days. They started working together and after 12 days, c joined them and the whole job finished in 15 days. How much time would c require to complete the job if only i was hired

Answer 1

here A and B took job for 20 days

A+B=20.....1

A+B+C=12.....2

Answer 2

Concept

Work and time sums are a basic sum of the proportionality concept. We take work done in 1 day and proceed accordingly.

Given

A and B complete the work together in 20 days. They work for 12 days after which C joins them and the work is completed in 15 days.

To Find

We are asked to find in how many days will C complete the work individually.

Solution

First, we find the work done by A and B together in 1 day.

A + B in 20 days complete 1 task, that is

(A+B) in 20 days = 1 task

Now, we find amount of task completed by them in 1 day,

(A+B) in 1 day = 1/20 task

∴ (A+B) in 12 days = 1/20 * 12 task = 12/20 task

Task left = 1 - 12/20 = 8/20

This left task is completed by A, B and C in three days, that is

(A + B + C) in 3 days = 8/20 task

or, (A + B + C) in 1 day = (8/20)/3 task = 8/60 task

Now, we can find how much task do C do in 1 day,

Work done by C in 1 day = (A + B + C) in 1 day - (A + B) in 1 day

= 8/60 - 1/20 task = 5/60 task = 1/12 task.

∴ C completes 1/12th of the task in 1 day,

or, C in 1 day = 1/12 task

or, C in 12 days = (1/12)*12 task = 1 task (Multiplying both sides with 12)

Hence C will take 12 days to complete the job individually.

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