Question

Two persons A and B could finish a work in p days. They worked together for q days. Then A was called off, and the remaining work was completed by B in r days. In how many days could each of them do it?​

Answer 1

$\huge\sf\pink{Answer}$

☞ $\sf \dfrac{1}{x} = \dfrac{r-p+q}{pr}$

☞ $\sf \dfrac{1}{y} = \dfrac{p-q}{pr}$

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$\huge\sf\blue{Given}$

✭ Two persons A & B could complete a work in p days

✭ Number of days they worked together is q

✭ After that A was off and B apne had to complete the work, he took r days

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$\huge\sf\gray{To \:Find}$

◈ Number of days taken be reach of them?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

◕ Work done by A be x

◕ Work done by B be y

☯ $\underline{\sf As \ Per \ the \ Question}$

Both A & B work for a time p so then in one day,

≫ $\sf \dfrac{1}{x}+\dfrac{1}{y} = \dfrac{1}{p} \:\:\: -eq(1)$

So if they work for q days,then they both will complete,

»» $\sf q\times \dfrac{1}{p}$

»» $\sf \dfrac{q}{p}$

If total work was 1

➳ $\sf 1-\dfrac{q}{p}$

➳ $\sf \dfrac{p-q}{p}$

Given that B works for r days, then work done by B will be,

➝ $\sf \dfrac{1}{y} = \dfrac{\dfrac{p-q}{p}}{r}$

➝ $\sf \dfrac{1}{y} = \dfrac{p-q}{p\times r}$

➝ $\sf \red{\dfrac{1}{y} = \dfrac{p-q}{pr}}$

From eq(1)

➝ $\sf \dfrac{1}{x} = \dfrac{1}{p} - \dfrac{p-q}{pr}$

➝ $\sf \dfrac{1}{x} = \dfrac{r-(p-q)}{pr}$

➝ $\sf \orange{\dfrac{1}{x} = \dfrac{r-p+q}{pr}}$

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