Time and Work

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When Abhinav and Bipul are working alone, they can complete a piece of work in 25 days and 30 days respectively. On day 1, Bipul started the work and Abhinav joined B from day 3 on-wards. Find after how many days will the work be completed?









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Option(C) is correct

Fraction of work completed by Abhinav in one day = \(\dfrac{1}{25}\)

Fraction of work completed by Bipul in one day = \(\dfrac{1}{30}\)

Fraction of work completed by Bipul on day1 and day 2 = \(2\left(\dfrac{1}{30}\right)=\dfrac{1}{15}\)

Fraction of work left after 2 days = \(1-\dfrac{1}{15}=\dfrac{14}{15}\)

Fraction of work completed by Both = \(\dfrac{1}{25}+\dfrac{1}{30}=\dfrac{11}{150}\)

Number of days after day 2 to complete work = \(\dfrac{14/15}{11/150}=12.72\) days

So after $2+13$ = 15 days works will be completed.

Edit: For an alternative method, check comment by Vejayanantham TR.

(4) Comment(s)

Amber Singh

deepak bro i also feel same way but what can i do i have to crack Elitmus with good marks

Vejayanantham TR

Alternate method,

Let $x$ be total days of work,

Two days of work of Bipul $= \dfrac{1}{15}$

Remaining days $= x-2$

So, $\dfrac{1}{15} + (x-2) \left( \dfrac{1}{25} + \dfrac{1}{30} \right) = 1$ (unitary method)

$\dfrac{1}{15} \left(1 + (x-2) \dfrac{55}{50} \right) =1$

$\dfrac{1}{15} * \dfrac{( 50 + 55x -110)}{50} =1$

$55x-60 = 50*15$

$x= \dfrac{810}{55}$

$= 14.72$

$= 15$

Chirag Goyal

Instead of $15 \text{ days}$

Could you just update the option to $14\dfrac{8}{11}$ Days?


Ideally, this should be updated to the value you've specified, i.e. $14\dfrac{8}{11}$ days. But for the sake of simplicity it has been converted to a round number of days.

Such questions are asked in the exams and I like to let it pass.