Question

While doing some work, the efficiency of A is equal to the average of the efficiency of C and twice the efficiency of B. The efficiency of B is equal to the average of the efficiency of C and half the efficiency of A. What is the ratio of the efficiencies of A and B?

• A. 17 : 18
• B. 8 : 5
• C. 14 : 15
• D. 51 : 41
• E. None of these

Answer 1

The correct option is B 8 : 5

$A=\frac{2B+C}{2}=2A=2B+C\to \left(1\right)$

$B=\frac{\frac{1}{2}\left(A\right)+C}{2}$

$\Rightarrow 2B=\frac{A+2C}{2}$

⇒ 4B = A + 2C

So, A = 4B – 2C → (2)

From (1), 4A = 4B + 2C → (3)

⇒ 2C = 4A – 4B – A {from (2) and (3)}

⇒ 5A = 8B

$\Rightarrow \frac{A}{B}=\frac{8}{5}$