Question

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish the work in 14 days. find the time taking by 1 man alone and 1 boy alone to finish the same work. Solve using elimation method

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the work done by 1 men in 1 day be x.

And the work done by 1 boy in 1 day be y.

According to the Question,

⇒ 8x + 12y = 1/10 ..... (i)

⇒ 6x + 8y = 1/14 .....(ii)

Multiplying Eq (i) with 2 and Eq (ii) with 3, we get

⇒ 16x + 24y = 1/5 ....(iii)

⇒ 18x + 24y = 3/4 .....(iv)

Subtracting Eq (iii) and (iv), we get

16x + 24y = 1/5

18x + 24y = 3/4

___________

-      -         -

⇒ - 2x = 1/5 - 3/4

⇒ - 2x = 14 - 15/70

⇒ - 2x = - 1/70

⇒ x = 1/140

Putting x's value in Eq (i), we get

⇒ 8x + 12y = 1/10

⇒ 8(1/140) + 12y = 1/10

⇒ 12y = 1/10 - 8/140

⇒ 12y = 14 - 8/140

⇒ 12y = 6/140

⇒ y = 1/280

Hence, 1 one men will complete the work in 140 days and 1 boy will complete the work in 280 days.

Answer 2

Answer:

Let the Strength of 1 man be M and Strength of 1 Boy be B.

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf Work=Work\\\\\\:\implies\sf (8Men + 12Boys) \times 10Days = (6Men +8Boys) \times 14Days\\\\{\scriptsize\qquad\bf{\dag}\:\:\text{Dividing both term by 2 Days}}\\\\:\implies\sf (8M+12B)5=(6M+8B)7\\\\\\:\implies\sf 40M+60B=42M+56B\\\\\\:\implies\sf 60B-56B=42M-40M\\\\\\:\implies\sf 4B=2M\\\\\\:\implies\sf \dfrac{B}{M}=\dfrac{2}{4}\\\\\\:\implies\sf \dfrac{B}{M}=\dfrac{1}{2}\\\\\\:\implies\sf B:M=1:2$

• Ratio of Strength of Boy to Man is 1 : 2.
• That's why Ratio of Time will be 2 : 1 of Boy to Man.
• Now we will use this Ratio in Above Equation to find Days.

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{One Man will take :}}$

$\dashrightarrow\sf\:\:(8Men+12Boys) \times 10Days=1Man \times Days\\\\\\\dashrightarrow\sf\:\:(8M+12B) \times 10=1M \times Days\\\\\\\dashrightarrow\sf\:\:(8 \times 2+12 \times 1) \times 10=1 \times 2 \times Days\\\\\\\dashrightarrow\sf\:\:(16+12) \times 5=Days\\\\\\\dashrightarrow\sf\:\:28 \times 5=Days\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Days_{(Man)}=140\:Days}}$

⠀

$\therefore\:\underline{\textsf{1 Man Alone can do work in \textbf{140 Days}}}.$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{One Boy will take :}}$

• As Ratio of Time of B : M = 2 : 1
• That's why we can use it as :

$\dashrightarrow\sf\:\:Boy=Man_{(Days)}\times\dfrac{B}{M}\\\\\\\dashrightarrow\sf\:\:Boy=140Days\times \dfrac{2}{1}\\\\\\\dashrightarrow\sf\:\:Boy=140Days\times 2\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Days_{(Boy)}=280\:Days}}$

⠀

$\therefore\:\underline{\textsf{1 Boy Alone can do work in \textbf{280 Days}}}.$

$\rule{100}{2}$

• This is Ratio Method, As Elimination Method is already Solved Above.