A and B together complete a work in 8 days. If B is 25% more efficient than A, then in how many days will A alone complete the same work?

Correct option is C

Given: 

A and B worked together = 8 days

B is 25% more efficient than A

Formula used:
Days = $$\frac{\text{Work}}{\text{ Efficiency}}$$​​

Solution:

Let's denote the efficiency of A as 'a'

Since B is 25% more efficient than A, B's efficiency is 1.25a

If they work together for 8 days, they complete the work.

So, 8 $$\times$$​ (a + 1.25a) = 1 (considering the whole work as 1 unit)

8 $$\times$$​ 2.25a = 1

a = $$\frac{1}{(8\times 2.250)}$$​ 

a = $$\frac{1}{18}$$​​

Now, to find the days A alone takes to complete the work:

Days = $$\frac{\text{Work}}{\text{ Efficiency}}$$ ​

Days = $$\frac{1}{\frac{1}{18}}$$ = 18​

Therefore, A alone can complete the work in 18 days.

Alternate Solution:

Work Efficiency ratio of A and B; 

= 100 : 125

 = 4 : 5 

Work done by A and B work together for 8 days = (4 + 5) × 8 = 72 unit work

A alone can complete the work in : $$\frac{72}{4}$$ = 18 days