Question

4 painters are required to paint a house in 5 days.
1. how many painters are needed to paint house in 1 day.
2. Two of them fall ill before the work started,how long will the job take


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Answer 1

Step-by-step explanation:

Total work = 4 X 5 = 20

1. Number of painters = Total work ÷ Number of days

or, 20 ÷ 1 = 20 painters.

2. Since two of them are ill, so now only 2 painters will complete whole work in

20 ÷ 2 = 10 days.

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Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 4\: painters \:are\: required\: to\: paint\: a\: house\: in\: 5\: days.$

$\tt 1) \:How\: many \:painters\: are\: needed\: to\: paint\: house\\\tt in \:1\: day.$

$\tt 2)\: Two\: of\: them\: fall \:ill \:before\: the\: work\: started,\:how\\\tt long\: will\: the\: job\: take$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf 4\: painters \:are\: required\: to\: paint\: a\: house\: in\: 5\: days.$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\sf \bf 1) \:How\: many \:painters\: are\: needed\: to\: paint\: house \: in \:1\: day.$
• $\sf \bf 2)\: Two\: of\: them\: fall \:ill \:before\: the\: work\: started,\:how \: long\: will\: the\: job\: take$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\color {springgreen} \underline {\sf 1) \:How\: many \:painters\: are\: needed\: to\: paint\: house \:in \:1\: day.}}$

${\color{gold}{\mathfrak {Let \: the \: number \: of \: painters \:required\: be \: x}}}$

${\color {blue} {\boxed {\boxed {\boxed { \color{green}{\sf \bf a:b::c:d\longrightarrow \dfrac{a}{b} = \dfrac{c}{d}}}}}}}$

$\sf \bf \implies 4:1::x:5$

$\sf \bf \implies \dfrac{4}{1}=\dfrac{x}{5}$

$\sf \bf \implies 1 \times x = 4 \times 5$

$\sf \bf \implies 1x=20$

$\sf \bf \implies x=\dfrac{20}{1}$

$\implies {\color {orange} {\boxed {\boxed {\color {aqua} {\sf \bf x=20 \:painters}}}}}$

${\underbrace {\color {red} {\underline {\color {red} {\overline {\color {red} {\sf \therefore 20 \:painters\: are\: needed\: to\: paint\: house \: in \:1\: day}}}}}}}$

—————————————————————————————

${\color {springgreen} \underline {\sf 2)\: Two\: of\: them\: fall \:ill \:before\: the\: work\: started,\:how \: long\: will\: the\: job\: take.}}$

${\color{gold}{\mathfrak {Let \: the \: number \: of \: days \:required\: be \: x}}}$

${\color {blue} {\boxed {\boxed {\boxed { \color{green}{\sf \bf a:b::c:d\longrightarrow \dfrac{a}{b} = \dfrac{c}{d}}}}}}}$

$\sf \bf \implies 4:2::x:5$

$\sf \bf \implies \dfrac{4}{2}=\dfrac{x}{5}$

$\sf \bf \implies 2 \times x = 4 \times 5$

$\sf \bf \implies 2x= 20$

$\sf \bf \implies x=\dfrac{20}{2}$

$\sf \bf \implies x=\dfrac{\cancel {20}}{\cancel {2}}$

$\implies {\color {orange} {\boxed {\boxed {\color {aqua} {\sf \bf x= 10 \:days}}}}}$

${\underbrace {\color {red} {\underline {\color {red} {\overline {\color {red} {\sf \therefore 10\:days \:are \:needed \:if\:2 \:workers \:become \:ill\:before \:starting \:the \:work}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

___________________________________________

$\sf \bf\huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

${\color {brown} {\sf Identity}}$

$\sf \bf a:b::c:d\longrightarrow \dfrac{a}{b} = \dfrac{c}{d}$