Question

A alone would take 27 hours more to complete the job than if both a and b would together.if b worked alone,he took 3 hours more to complete the job than a and b worked together.what time, would they take if both a and b worked together

Answer 1

Let( A+B )together take x hrs
A will take x +27hrs
B will take x +3 hrs
Total work =(x+ 27)(x+3)
Efficiency A = x +3
B= x+27
Total efficiency=2x+30
Time working together =(x+27)(x+3)/2x+30=x
${x}^{2} + 30x + 81 = 2 {x}^{2} + 30x \\ or \: {x}^{2} = 81 \\ = x = 9hrs$

Answer 2

Answer:

9 hours is the correct answer.

Step-by-step explanation:

Let (A + B) together take x hrs

A will take x + 27 hrs

B will take x + 3 hrs

Total work = (x+ 27) × (x+3)

Efficiency of A = x + 3

Efficiency of B = x + 27

Total efficiency = 2·x + 30

$\text{Time working together = }\frac{(x + 27)\cdot (x + 3)}{2\cdot x+30}=x\\\\\implies x^2+30\cdot x+81=2\cdot x^2+30\cdot x\\\\\implies x^2=81\\\\\implies\bf x = 9\thinspace{ hours}$