Question

soumya takes 6 days less than number of days by bhagya to complete a piece of work. if both together can complete same work in 4 days how many days will bhagya alone complete the work​

Answer 1

thanks for asking the question

Answer 2

Answer:

Bhagya alone complete the work in 12 days.

Step-by-step explanation:

Let x be the no of days taken by Soumya and y be the no of days taken by Bhagya.

according to the question,

x = y - 6 ............... (1)

$\frac{1}{x}+\frac{1}{y}=\frac{1}{4}$ ............(2)

Value of x from (1), put in (2)

we get,

$\frac{1}{y-6}+\frac{1}{y}=\frac{1}{4}$

$\frac{y+y-6}{y(y-6)}=\frac{1}{4}$

$4(2y-6)=y^2-6y$

$8y-24=y^2-6y$

$y^2-6y-8y+24=0$

$y^2-14y+24=0$

$y^2-12y-2y+24=0$

$y(y-12)-2(y-12)=0$

$(y-12)(y-2)=0$

⇒ y = 2 & 12

when y = 2 we get x = 2 - 6 = -4 which is not possible

when y = 12 we get x = 12 - 6 = 6

Therefore, Bhagya alone complete the work in 12 days.