Question

A and B working together can do a work in 6 days.If A takes 5 days less than B to finish the work,in how many days B alone can do the work ?

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Answer 1

Answer: 15 days

Step-by-step explanation: please find the attachment

Hope it helps

Answer 2

Given :

A and B working together can do a work in 6 days

To Find :

If A takes 5 days less than B to finish the work,in how many days B alone can do the work ?

Solution:

Let x be the no. of days taken by B to complete the work

A takes 5 days less than B to finish the work

So, A completes work in x-5 days

(A+B)'s 1 day work =$\frac{1}{x}+\frac{1}{x-5}$

(A+B)'s 6 days work =$6( \frac{1}{x}+\frac{1}{x-5})$

We are given that A and B working together can do a work in 6 days

So,$6( \frac{1}{x}+\frac{1}{x-5})= 1\\6(\frac{x-5+x}{x(x-5)})=1\\6(\frac{2x-5}{x(x-5)})=1\\12x-30=x^2-5x\\x^2-17x+30=0\\x^2-15x-2x+30=0\\(x-15)(x-2)=0\\x=15,2$

If B Complete work in 2 days

So, A completes work in day = x-5 = 2-5 = -3

No. of days cannot be negative

So, B completes work alone in 15 days