4men clear a farm for 8 days and are paid 24$ How long will 6 men take to clear the same farm if they are paid 360$ ?


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Question Number 162951 by Ar Brandon last updated on 02/Jan/22

$4 men clear a farm for 8 days and are paid 24 $$ $How long will 6 men take to clear the same farm$ $if they are paid 360 $ ?$
Commented by mr W last updated on 03/Jan/22

$4 m e n e a r n i n 8 d a y s 24 $ . \Rightarrow o n e m a n i n o n e d a y : \frac{24}{4 \times 8}$ $6 m e n e a r n i n x d a y s 360 $ . \Rightarrow o n e m a n i n o n e d a y : \frac{360}{6 x}$ $s i n c e {i t}^{'} s a c o n s t a n t h o w m u c h o n e m a n$ $e a r n s i n o n e d a y (w e m u s t a s s u m e,$ $o t h e r w i s e n o t s o l v a b l e),$ $\frac{24}{4 \times 8} = \frac{360}{6 x}$ $\Rightarrow x = 80 d a y s$
Commented by Ar Brandon last updated on 03/Jan/22
Got it now. Thanks Sir.
	Answered by Rasheed.Sindhi last updated on 02/Jan/22

	$\begin{array}{ccc} men & days & $ \\ 4 & 8 & 24 \\ 6 & x & 360 \end{array}$ $x : 8 :: {\begin{cases} 4 : 6 \\ 360 : 24 \end{cases}$ $x \times 6 \times 24 = 8 \times 4 \times 360$ $x = \frac{8 \times 4 \times 360}{6 \times 24} = 80 days$
	Commented by Ar Brandon last updated on 02/Jan/22
	Really?! OK Sir. Thanks
	Commented by Ar Brandon last updated on 02/Jan/22
	Is this some sort of cross-multiplication?
	Commented by Rasheed.Sindhi last updated on 03/Jan/22
	$The problem is somewhat strange. It is not dependant on amount of work! determinant (((men),(days),$),((4_6 ↓),(8_x ↑),(24_(360) ↑)),((men increase_(→days decrease_((inverse proportion)) ) ),,(dollars increase_(→days increase_((direct proportion)) ) )),((4:6),(x:8),(360:24)),((x:8::4:6_(A) ),,(x:8::360:24_(B) ))) A∪B: x:8:: { ((4:6)),((360:24)) :} x×6×24=8×4×360 x=((8×4×360)/(6×24))=80 days$
	$T h e p r o b l e m i s s o m e w h a t s t r a n g e .$ $I t i s n o t d e p e n d a n t o n a m o u n t o f$ $w o r k!$ $\begin{array}{ccccc} men & days & $ \\ \underset{6}{4} ↓ & \underset{x}{8} ↑ & \underset{360}{24} ↑ \\ \underset{\underset{(i n v e r s e p r o p o r t i o n)}{\to d a y s d e c r e a s e}}{m e n i n c r e a s e} & \underset{\underset{(d i r e c t p r o p o r t i o n)}{\to d a y s i n c r e a s e}}{d o l l a r s i n c r e a s e} \\ 4 : 6 & x : 8 & 360 : 24 \\ \underset{A}{\underset{⏟}{x : 8 :: 4 : 6}} & \underset{B}{\underset{⏟}{x : 8 :: 360 : 24}} \end{array}$ $A \cup B :$ $x : 8 :: {\begin{cases} 4 : 6 \\ 360 : 24 \end{cases}$ $x \times 6 \times 24 = 8 \times 4 \times 360$ $x = \frac{8 \times 4 \times 360}{6 \times 24} = 80 days$
	Commented by Rasheed.Sindhi last updated on 03/Jan/22

	$T h i s i s b y^{'} p r o p o r t i o n {m e t h o d}^{'} w h i l e$ $s i r m r W^{'} s m e t h o d (c o m m e n t t o$ $t h e q u e s t i o n) i s^{'} u n i t a r y {m e t h o d}^{'}$ $T h i s i s a c o m p o u n d p r o p o r t i o n .$
	Commented by Rasheed.Sindhi last updated on 03/Jan/22

	$S i r, p l r e a d m y a b o v e c o m m e n t a g a i n$ $a s I^{'} v e e d i t e d i t b e f o r e r e c e i v i n g y o u r$ $c o m m e n t .$
	Commented by Rasheed.Sindhi last updated on 03/Jan/22

	$I h a v e a l s o s a m p a t h y f o r t h e m :)$ $B u t s i r, t h e q u e s t i o n s a y s :$ $4 m e n . . . . . ∣ 6 m e n . . . . . . c l e a r s a m e f a r m .$ $t h a t i s d o s a m e q u a n t i t y o f w o r k .$
	Commented by mr W last updated on 03/Jan/22

	$‘ ‘ c l e a r t h e s a m e {f a r m}^{″} {d o e s n}^{'} t d e f i n e$ $t h e q u a n t i t y o f t h e w o r k, o n l y t h e$ $t y p e o f t h e w o r k, i t h i n k . i t c o u l d b e$ $t h a t t h e 4 m e n c l e a r e d t h e f i r s t 120 m^{2}$ $o f t h e f a r m i n 8 d a y s f o r t o t a l l y 24 $,$ $a n d t h e 6 m e n c l e a r e d t h e r e m a i n i n g$ $1800 m^{2} o f t h e s a m e f a r m i n 80 d a y s$ $f o r t o t a l l y 360 $ . t h e s a m e f a r m p a y s$ $t h e s a m e m o n e y f o r e a c h m a n a n d$ $e a c h d a y . d i f f e r e n t f a r m s m a y p a y$ $l e s s o r m o r e . t h e r e f o r e i t m a k e s$ $s i n s e t o s t a t e t h a t t h e y c l e a r e d t h e$ $s a m e f a r m . t h i s i s m y o p i n i o n .$
	Commented by mr W last updated on 03/Jan/22

	$b u t n o m a t t e r h o w i t i s, 4 m e n e a r n$ $o n l y 24 $ i n 8 d a y s, {t h a t}^{'} s d e f i n i t e l y$ $t o o l e s s, i t h i n k :)$
	Commented by Rasheed.Sindhi last updated on 03/Jan/22

	$Okay sir, {y o u}^{'} r e k e e n o b s e r e r, n o d o u b t!$ $‘ ‘ 4 men clear a farm . . .^{″} m e a n s t h e y$ $c l e a r w h o l e f a r m . ‘ ‘ . . . 6 men take$ $to clear the same {farm}^{″}, {d o e s n}^{'} t a g a i n i t$ $m e a n t h e w h o l e f a r m ?$
	Commented by mr W last updated on 03/Jan/22

	$a c t u a l l y i t h o u g h t t h e s a m e a s y o u .$ $b u t t h e n i g o t a p r o b l e m w i t h t h e l o g i c .$ $s o i j u s t c h a n g e d m y o p i n i o n i n o r d e r$ $t o b e c o m e c o n f o r m w i t h t h e s o l u t i o n .$
	Commented by mr W last updated on 03/Jan/22

	$t h i s i s t h e l o g i c p r o b l e m i m e n t i o n e d .$ $‘ ‘ c l e a r a {f a r m}^{″} a n d ‘ ‘ c l e a r t h e s a m e$ ${f a r m}^{″} m a y n o t m e a n t h e s a m e w o r k$ $d o n e, b e c a u s e o n e c a n n o t p a y f o r t h e$ $s a m e w o r k d o n e i n o n e t i m e o n l y 24 $$ $a n d i n a n o t h e r t i m e 360 $ . c e r t a i n l y$ $i n r e a l i t y {i t}^{'} s p o s s i b l e, b u t i n$ $m a t h e m a t i c s {i t}^{'} s n o t p o s s i b l e .$ $b e c a u s e t h e r e i s n o m a t h e m a t i c s i f$ $t h e r e i s n o l i g i c . t h e r e f o r e ‘ ‘ c l e a r a$ ${f a r m}^{″} a n d ‘ ‘ c l e a r t h e s a m e {f a r m}^{″}$ $c a n l o g i c a l l y o n l y m e a n t h e t y p e o f$ $t h e w o r k, i . e . ‘ ‘ c l e a r i n a {f a r m}^{″} a s$ $w e l l a s ‘ ‘ c l e a r i n t h e s a m e {f a r m}^{″} .$ $i t h i n k t h e g u y w h o o r i g i n a l l y w r o t e$ $t h i s q u e s t i o n i s n o l a w y e r, e v e n n o$ $n a t i v e s p e a k e r o f e n g l i s h, l i k e y o u$ $a n d m e . t h e r e f o r e w e s h o u l d l o o k m o r e$ $a t t h e l o g i c b e h i n d i t i n s t e a d o f t h e$ $w o r d i n g .$
	Commented by Rasheed.Sindhi last updated on 03/Jan/22

	$T_{H_{AN} K} S S_{I_{R!}}$ 👍👍👍👍👍
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