Question 101

# A and B can complete a piece of work in 24 days while B and C can complete the same work in 30 days. If A works twice as much as C, then the numberof days required for B alone to complete the work is

Solution

Let A can finish a work in x days, B can finish the work in y days.

A and B can finish the work in one days$$=\dfrac{1}{24}$$

$$\dfrac{1}{2x}+\dfrac{1}{y}=\dfrac{1}{24}----------------(i)$$

A works twice as much as C.

Hence C can finish the work in $$=2x$$

Hence C can finish the work in one days $$=\dfrac{1}{2x}$$

B and C can finish the work$$=30days$$

Hence, B and C can finish the work in one days$$\dfrac{1}{y}+\dfrac{1}{2x}=\dfrac{1}{30}-----------(ii)$$

From the equation (i) and (ii)

$$\Rightarrow \dfrac{1}{24}-\dfrac{1}{x}+\dfrac{1}{2x}=\dfrac{1}{30}$$

$$\Rightarrow \dfrac{1}{24}-\dfrac{1}{2x}=\dfrac{1}{30}$$

$$\Rightarrow \dfrac{1}{2x}=\dfrac{1}{24}-\dfrac{1}{30}$$

$$\Rightarrow \dfrac{1}{2x}=\dfrac{5-4}{120}=\dfrac{1}{120}$$

$$\Rightarrow x=60$$days

Hence, $$\dfrac{1}{y}=\dfrac{1}{24}-\dfrac{1}{60}=\dfrac{5-2}{120}=\dfrac{3}{120}$$

$$\Rightarrow y=40$$days.