Question

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. how long will theh together take to complete the work?​

Answer 1

Given :

• X can do a piece of work in 40 days.He works at it for 8 days and then Y finished it in 16 days.

To Find :

• how long will theh together take to complete the work?

Solution:

❍ Now,

• Let the total work to be done be 1

${\underline{\bf{\bigstar According \: to\: the\: question}}}$

• X can finish the work in 40 days
• He worked for 8 days and left

 ✦ So, let's find the work he completed

$\longrightarrow \tt \: 1 : 40 = A \: : 8 \\ \\ \\ \longrightarrow \tt 40 \times A =1 \times 8 \\ \\ \\ \longrightarrow \tt A = \cancel\frac{8}{40} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt A = \frac{1}{5} \bigstar \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth he completed 1/5 th part of the work in 8 days

 ✦ Now let's find the work to be done

$\dashrightarrow \tt 1 - \frac{1}{5} \\ \\ \\ \dashrightarrow \tt \frac{5}{5} - \frac{1}{5} \\ \\ \\ \dashrightarrow \tt \frac{4}{5} \bigstar \: \: \:$

• Henceforth, 4/5 th part of the work is yet to be completed.

${\underline{\frak{As\: we\: know \:that}}}$

• Y completes the remaining work in 16 days

 ✦ So,

• Y completes 4/5 th work in 16 days

★ Now,

• Let's find Y's 1 day work

$\dashrightarrow \tt \: Y _{(1 \: day \: work)} = \frac{4}{5} \div 16 \\ \\ \\\dashrightarrow \tt \: Y _{(1 \: day \: work)} \frac{ \dfrac{4}{5} }{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \dashrightarrow \tt \: Y _{(1 \: day \: work)} = \frac{4}{5} \times \frac{1}{16} \\ \\ \\ \dashrightarrow \tt \: Y _{(1 \: day \: work)} = \frac{1}{20} \bigstar \: \: \:$

 ✦ And

$\dashrightarrow \tt \: X _{(1 \: day \: work)} = 1 \div 40 \\ \\ \\ \dashrightarrow \tt \: X _{(1 \: day \: work)} = \frac{1}{40} \bigstar \:$

➱ So,

• Their 1 day work when they work together will be

$\longrightarrow \tt \frac{1}{x} + \frac{1}{y} \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \frac{1}{40} + \frac{1}{20} \\ \\ \\ \longrightarrow \tt \frac{1}{40} + \frac{2}{40} \\ \\ \\ \longrightarrow \tt \frac{3}{40} \bigstar \: \: \: \: \: \:$

★ Now,

• The total time taken taken to complete the work will be

$\longrightarrow \tt inverse \: of \: \frac{3}{40} days \\ \\ \\ \longrightarrow \tt \frac{40}{3} days \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow { \boxed{ \pmb{ \frak{ 16 \frac{2}{3} days }}}\bigstar } \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

• They will take 16 2/3 days when they work together

━━━━━━━━━━━━━━━━━━━━━━