Question

8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time
one girl alone that by one boy alone to finish the work.
​

Answer 1

The time one girl alone finish the work in 140 days and one boy alone finish the work in 280 days.

Step-by-step explanation:

Let the time taken by girls be “x” days and the time taken by boys be “y” days.

So,

Work done by 1 girl in 1 day = 1/x

work done by 1 boy in 1 day = 1/y

According to the question, we can write the eq. as,

8/x + 12/y = 1/10 ............ (i)

and

6/x + 8/y = 1/14 .......... (ii)

Let’s consider u = 1/x & v = 1/y, so we can rewrite the eq, as,

8u + 12v = 1/10 ......... (iii)

and

6u + 8v = 1/14 ........... (iv)

Now, on multiplying eq. (iii) by 2 & eq. (iv) by 3 and subtracting the equations we get,

18u + 24v = 3/14

16u + 24v = 2/10

-      -             -

----------------------------

   2u = 1/70

-------------------------

  u = 1/140

Substituting the value of u = 1/140 in eq. (iii), we get

(8*1/140) + 12v = 1/10

⇒ 2/35 + 12v = 1/10

⇒ 12v = 1/10 – 2/35

⇒ 12v = [35 - 20] / [35*10]

⇒ v = 15 / [35*10*12]

⇒ v = 1/280  

Since we have,

u = 1/x

⇒ 1/140 = 1/x

⇒ x = 140

and,

v = 1/y

⇒ 1/280 = 1/y

⇒ y = 280

Thus, one girl can alone complete the work in 140 days and one boy can alone complete the work in 280 days.

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Also View:

If 7 man or 8 woman or 10 boys can finish a piece of work in 24 days of 9 hours, find how many men with the help of 4 woman and 5 boys can finish it in 18 days of 6 hours ?

https://brainly.in/question/4655979

If 3 women or 5 girls take 17 days to complete a piece of work, how long will 7 women and 11 girls working together take to complete the work?

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Answer 2

$\rule{261}{2}$

Let the time taken by the girls be x days, and the time taken by the boys be y days.Then,

♣ Time taken by 1 girl = 1/x days

♣ Time taken by 1 boy = 1/y days

Given that,

• Time taken by 8 girls and 12 boys = 10 days

• Time taken by 6 girls and 8 boys = 14 days

So we can say that,

♣ 8/x + 12/y = 1/10

♣ 6/x + 8/y = 1/14

Let 1/x = u, and 1/y = v.

⇢ 8u + 12v = 1/10               ...(i)

⇢ 6u + 8v = 1/14                ...(ii)

Multiplying 6 with eq.(i) and 8 with eq.(ii) and subtracting :-

$\displaystyle{ 48u + 72v = \frac{6}{10} }\\-\\\displaystyle{48u + 64v = \frac{8}{14} }\\\rule{80}{1}\\8v=\frac{6}{10}- \frac{8}{14}$

On solving it :-

$\displaystyle{\implies 8v= \frac{3}{5} -\frac{4}{7} }\\\\\implies 8v=\frac{21-20}{35} \\\\\implies 8v=\frac{1}{35} \\\\\implies v=\frac{1}{280} \\\\\implies v=\frac{1}{y}=\frac{1}{280} \\\\\boxed{\implies y=280\ days}$

Now, putting the value of v = 1/280 in eq.(i) :-

$\displaystyle{8u+12v=\frac{1}{10} }\\\\\displaystyle{\implies 8u+\frac{12}{280} =\frac{1}{10} }\\\\\displaystyle{\implies 8u+\frac{3}{70}=\frac{1}{10} }\\\\\displaystyle{\implies 8u=\frac{1}{10}-\frac{3}{ 70} }\\\\\displaystyle{\implies 8u=\frac{7-3}{70}}\\\\\displaystyle{\implies 8u=\frac{4}{70} }\\\\\displaystyle{\implies u=\frac{4}{560} }\\\\\displaystyle{\implies u=\frac{1}{140} }\\\\\displaystyle{\implies u=\frac{1}{x}=\frac{1}{140} }\\\\\boxed{\displaystyle{\implies x=140\ days}}$

➥ So, the time taken by one girl is 140 days and the time taken by one boy is 280 days.

$\rule{261}{2}$