Question

A B and C can complete a work in 5 days if a and c can complete the same work in 7.5 days and A alone in 15 days then in how many days can B and C finish the work?

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Answer 1

AnswEr :

$\frak{Given}\begin{cases}\texttt{A + B + C = 5 Days}\\\texttt{A + C = 7.5 Days}\\\texttt{A = 15 Days}\end{cases}$

$\underline{\bigstar\:\textsf{C can do work in :}}$

$:\implies\tt A+C =\dfrac{A \times C}{A+C}\\\\\\:\implies\tt 7.5=\dfrac{15 \times C}{15+C}\\\\\\:\implies\tt \dfrac{15}{2}=\dfrac{15 \times C}{15+C}\\\\\\:\implies\tt \dfrac{1}{2}=\dfrac{C}{15+C}\\\\\\:\implies\tt 15+C=2C\\\\\\:\implies\tt 15=2C-C\\\\\\:\implies\tt C=15\:Days$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{B can do work in :}}$

$:\implies\tt B = \dfrac{(A+C) \times (A+B+C)}{(A+C)-(A+B+C)}\\\\\\:\implies\tt B = \dfrac{7.5 \times 5}{7.5-5}\\\\\\:\implies\tt B =\dfrac{7.5 \times 5}{2.5}\\\\\\:\implies\tt B =3 \times 5\\\\\\:\implies\tt B =15\:Days$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{(B + C) can do work in :}}$

$\dashrightarrow\:\:\tt B+C=\dfrac{B \times C}{B+C}\\\\\\\dashrightarrow\:\:\tt B+C=\dfrac{15 \times 15}{15+15}\\\\\\\dashrightarrow\:\:\tt B+C= \dfrac{15 \times 15}{15 \times 2}\\\\\\\dashrightarrow\:\:\tt B+C= \dfrac{15}{2}\\\\\\\dashrightarrow\:\: \underline{\boxed{\tt B+C=7.5 \:Days}}$

⠀

$\therefore\:\underline{\textsf{B \& C together will complete work in \textbf{7.5 Days}}}$

Answer 2

Answer:

A + C = AC/A + C

7.5 = 15C/15 + C

15 + C = 2C

C = 15 Days

Like that we got B = 15 Days.

• B + C work will be :

=> 15*15/15 + 15

=> 15*15/30

=> 15/2

=> 7.5 Days