Question

Q:25 Men working 8 hours a day produce 200 toys in 10 days.
In how many days 1000 toys will be produce by 100 men, if
they work 10 hours a day?​

Answer 1

$\sf\small\underline\red{Given:-}$

$\tt\small\underline{Case-(i)}$

$\tt{\implies No\:of\:man=25}$

$\tt{\implies No\:of\:toys=200}$

$\tt{\implies Total\:time\:taken=8*10=80\:h}$

$\tt\small\underline{Case-(ii)}$

$\tt{\implies No\:of\:man=100}$

$\tt{\implies No\:of\:toys=1000}$

$\tt{\implies Total\:time\:taken=?*10=10?\:h}$

$\sf\small\underline\red{To\: Find:-}$

$\tt{\implies No\:of\:days=?}$

$\sf\small\underline\red{Solution:-}$

$\tt{\implies Putting\:_{(case-(i))}=Putting\:_{(case-(ii))}}$

$\tt{\implies M\:_{(1)}\times\:T\:_{(1)}\times\:D\:_{(1)}=M\:_{(2)}\times\:T\:_{(2)}\times\:D\:_{(2)}}$

$\tt{\implies 25\times\:200\times\:80=100\times\:1000\times\:10?}$

$\tt{\implies 25\times\:2\times\:8=100\times\:10?}$

$\tt{\implies 400=1000?}$

$\tt{\implies ?=\dfrac{2}{5}\:days}$

$\sf\large{Hence,}$

$\tt{\implies No\:of\:days=10\times\:\dfrac{2}{5}=4\:days}$

$\sf\small\underline\red{Verification:-}$

$\tt{\implies M\:_{(1)}\times\:T\:_{(1)}\times\:D\:_{(1)}=M\:_{(2)}\times\:T\:_{(2)}\times\:D\:_{(2)}}$

$\tt{\implies 25\times\:200\times\:80=100\times\:1000\times\:4}$

$\tt{\implies 5000\times\:80=100000\times\:4}$

$\tt{\implies 400000=400000}$

$\tt{\implies Hence,\: verified:-}$

Answer 2

Answer:

Given :-

• 25 men working 8 hours a day produce 200 toys in 10 days.
• 1000 toys will be produce by 100 men in 10 hours a day.

To Find :-

• In how many days 1000 toys will be produce by 100 men, if they work 10 hours a day.

Solution :-

${\small{\bold{\purple{\underline{In\: the\: {1}^{{st}}\: case\: :-}}}}}$

Given :

• Total number of men = 25
• Total number of toys = 200
• Total time taken = 8 × 10 = 80 hours

${\small{\bold{\purple{\underline{In\: the\: {2}^{{nd}}\: case\: :-}}}}}$

Given :

• Total number of men = 100
• Total number of toys = 1000
• Total time taken = 10D hours

Now, according to the question :

$\implies \sf 25 \times 200 \times 80 =\: 100 \times 1000 \times 10D$

$\implies \sf 5000 \times 80 =\: 100000 \times 10D$

$\implies \sf 400000 =\: 1000000D$

$\implies \sf \dfrac{40000\cancel{0}}{100000\cancel{0}} =\: D$

$\implies \sf \dfrac{4000\cancel{0}}{10000\cancel{0}} =\: D$

$\implies \sf \dfrac{400\cancel{0}}{1000\cancel{0}} =\: D$

$\implies \sf \dfrac{40\cancel{0}}{100\cancel{0}} =\: D$

$\implies \sf \dfrac{4\cancel{0}}{10\cancel{0}} =\: D$

$\implies \sf \dfrac{\cancel{4}}{\cancel{10}} =\: D$

$\implies \sf \dfrac{2}{5} =\: D$

$\implies \sf\bold{\purple{D =\: \dfrac{2}{5}\: days}}$

Hence, the required day is :

$\dashrightarrow \sf Total\: time\: taken =\: {\cancel{10}} \times \dfrac{2}{\cancel{5}}$

$\dashrightarrow \sf Total\: time\: taken =\: 2 \times 2$

$\dashrightarrow \sf\bold{\red{Total\: time\: taken\: =\: 4\: days}}$

$\therefore$ In 2/5 days 1000 toys will be produce by 100 men, if they work 10 hours a day.