Question

16. 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 taken by the one girl alone that by one boy alone to finish the work.

Answer 1

Answer:

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.

Hope it helps you