Question

A is twice efficient as B. A and B together do the same work in as much time as C and D can do together. The ratio of the number of alone working days of C  to D is 2 : 3 and if B worked 16 days more than C then number of days which A worked alone? 
1. 18 days 
2. 17 days 
3. 16 days 
4. 14 days 
5. None of these

Answer 1

Correct Answer - Option 1 : 18 days 

Given 

Number of work C and D alone = 2 : 3

Formula Used 

Work = Time × Efficiency 

Calculation 

Let the working days for A, B, C and D are

A = x, B = 2x, C = 2y, D = 3y

Now, 1/x + 1/2x = 1/2y + 1/3y

⇒ 3/2x = 5/6y

⇒ 18y = 10x 

⇒ x : y = 9 : 5 

And 2x – 2y = 16

Now, solving both the equations, we get,

⇒ x = 18 days.

∴Number of days which A worked alone is 18 days.