Question

‘A’ can do a piece of work in x hours and B can do the same work in (x+5) hours. Working together they can do the same work in (x+1) hours, find x.

CLASS 10 MATHS CHAPTER QUADRATIC EQUATIONS

Answer 1

If someone finishes a work in 3 hours, then he does 1/3 of work every hour.

This means A works 1/x every hour, and B works 1/(x+5) every hour.

Their work will be added, and their work will equal to a person's who works 1/(x+1) every hour → 1/x + 1/(x+5) = 1/(x+1)

Since we cannot solve equations in this form, we will remove the denominator(there is no root formula in this form).

→ $\frac{2x+5}{x^2+5x} =\frac{1}{x+1}$

→ $(x+1)(2x+5)=x^2+5x$

→ $(2x^2+5x)+(2x+5)=x^2+5x$

→ $x^2+2x+5=0$ → Solutions are $-1\pm 2i$

There is no solution because they can't work 'complex number' hours.

Hope this helps.