Question

Babla alone can do a piece of work in 10 days ashu alone can do it in 15 days. The total wages for the work in rs.5000. How much should babla be paid off they work together for entire duration of the work?

Answer 1

$\mathfrak{Answer:}$

= Rs.3000 .

$\mathfrak{Step-by-Step\;Explanation:}$

$\underline{\bold{Given\;in\;the\;Question:}}$

• Babla can do a piece of work in 10 days.
• Ashu can do this work in 15 days.
• Total wages = Rs.5000.

$\mathbb{SOLUTION:}$

$\hookrightarrow\quad\textsf{If a can do a work in x days.}\\\\\hookrightarrow\quad\mathsf{Then\;a's\;one\;day\;work = \dfrac{1}{x}th\;part.}$

So

• Babla's one day work :

$\tt{=\dfrac{1}{10}th\;part.}$

• Ashu's one day work :

$\tt{=\dfrac{1}{15}th\;part.}$

We know that distribution of wages depend on the work efficiency.

Ratio of the share of Babla and Ashu :

$\tt{=\dfrac{1}{10}:\dfrac{1}{15}}\\\\\\\tt{=\dfrac{1}{10}\times 30:\dfrac{1}{15}\times 30}\\\\\\\tt{=3:2.}$

Let the Babla's and Ashu's share be Rs. 3x and Rs. 2x respectively.

$\mathfrak{According\;to\;Question:}\\\\\\\implies\tt{3x+2x=5000}\\\\\\\implies\tt{5x=5000}\\\\\\\implies\tt{x=\dfrac{5000}{5}}\\\\\\\therefore\quad\tt{x=1000.}$

$\bigstar\quad\textbf{Babla's share = 3x.}\\\\\\\tt{=3\times 1000}\\\\\\\tt{=Rs.3000.}\\\\\\\bigstar\quad\textbf{Ashu's share = 2x.}\\\\\\\tt{=2\times 1000}\\\\\\\tt{=Rs.2000.}\\\\\\\boxed{\boxed{\bold{Babla's\;Share=Rs.3000.}}}$