Question

Amit can do a piece of work in 24 days, bhuvan can do same work in 16 days, and chirang can do same job in 4/5 th time required by both amit and bhuvan. Amit and bhuvan work together for 6 days, then chirag completes the job. How many days did chirang work?

Answer 1

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Answer 2

Chirang did the work for 12 days.

Step-by-step explanation:

Given:

Amit (a) can do a work in 24 days

Bhuvan (b) can do the same work in 16 days

Chirang (c) can do same work in 4/5th time required by both (a) and (b).

a and b work together for 6 days, then c completed the work.

To find:

How many days did c work?

Solution:

1st We should know that in how many days c can complete the work

According to question,

Time required by both a and b = 16 + 24 = 40days

C can complete work = 4/5 × 40 = 32 days

Now, We will find how many work done by a and b in 6 days.

A complete a work in 24 days

________ 1/24 _____ 1 day

B complete a work in 16 days

_________ 1/16 ____ 1 day

So, Work done by both in 6 days,

$6(\frac{1}{24} + \frac{1}{16} )\\ \\ = 6(\frac{2 + 3}{48}) \: \: [\text{By taking L.C.M}] \\ \\ = 6 \times \frac{5}{48} \\ \\ = \frac{5}{8}$

Remaining work = 1 - 5/8 = 3/8

Now, Using rule of Three

Work________________Time(Day)

1 ____________________ 32

3/8 _____________________ ?

$\dfrac{ \dfrac{3}{8} }{ 1 } \times 32 \\ \\ = \frac{3}{8} \times 32 \\ \\ = \frac{3}{ \cancel{8}} \times \cancel{32} \\ \\ = 3 \times 4 \\ \\ = 12$

$\boxed{\text{ \therefore Chirang did the work for 12 days}}$