Question

If 24 painters working for 7 hours a day, for painting a house in 16 days. How many painters are required working for 8 hours a day will finish painting the same house in 12 days?​

Answer 1

$\Huge\mathfrak\purple{Solution:-}$

$\huge\sf\green{Given:-}$

$\sf\pink{24\:painters\:working\:for\:7\:hours\:a\:day,\:for}$$\sf\pink{painting\:a\:house\:in\:16\:days.}$

$\sf\green{Need\:to\:find:-}$

$\sf\orange{Painters\:are\:required\:working\:for\:8\:hour\:a}$$\sf\orange{day\:will\:finish\: painting\:the\:same\:house\:in\:12}$$\sf\orange{days?}$

$\sf\green{Step-by-step\:explanation:-}$

$\sf\red{24\:painters\:working\:for\:7\:hours\:a\:day\:to\:paint}$$\sf\red{a\:house\:in\:16\:days.}$

$\sf\pink{1\:painters\:working\:for\:7\:hours\:a\:day\:to\:paint}$$\sf\pink{the\:house\:in\:16×24\:days.}$

$\sf\purple{1\:painters\:working\:for\:1\:hours\:a\:day\:to\:paint}$$\sf\purple{the\:house\:in\:16×24×7days.}$

$\sf\red{Let\:the\:required\:number\:of\:painters\:be\:x\:then}$

$\sf\orange{x\:painters\:working\:for\:1\:hours\:a\:day\:to\:paint}$$\sf\orange{the\:house\:in\:(16×24×7)/x×days.}$

$\sf\blue{x\:painters\:working\:for\:8\:hours\:a\:day\:to\:paint}$$\sf\blue{the\:house\:in\:(16×24×7)/(x×8)days.}$

$\sf\green{But\:the\:numbers\:of\:days\:given=12}$

$\sf\pink{According\:to\:the\:problem:-}$

$\sf\red{(16\:×\:24\:×\:7)/(x\:×\:8)= 12}$

$\sf\orange{2688/8x\:=\:12}$

$\sf\red{8x\:×\:12=268}$

$\sf\orange{96x\:=\:2688}$

$\sf\red{96x\:=\:2688}$

$\sf\orange{x\:=\:2888/96}$

$\sf\red{x\:=\:28}$

Answer 2

If 24 painters working for 7 hours a day, for painting a house in 16 days. How many painters are required working for 8 hours a day will finish painting the same house in 12 days?

Solution:

24 painters working for 7 hours paint a house in 16 days.

1 painter working for 7 hours paints a house in 16 × 24 days.

1 painter working for 1 hour paints a house in 16 × 24 × 7 days.

Let the required number of painters be x, then;

x painters working for 1 hour a day paint the house in (16 × 24 × 7)/x days

x painters working for 8 hours a day paint the house in (16 × 24 × 7)/(x × 8) days

But the number of days given = 12

According to the problem;

(16 × 24 × 7)/(x × 8) = 12

2688/8x = 12

8x × 12 = 2688

96x = 2688

x = 2688/96

x = 28

Therefore, 28 painters working for 8 hours a day will finish the same work in 12 days.

Hope it helps uh✌️✌️