Efficiency of B is 37.5 percent less than A whereas efficiency of C is 60 percent less than B. A and C together can do a work in 42 days. Find how long all three will together take to complete the same work?

Correct option is D

​$$\text{Let the efficiency of A be } E_A \\[10pt]\textbf{Step 1: Find the efficiencies of B and C} \\[5pt]\text{Efficiency of B is 37.5\% less than A:} \\E_B = E_A \times \left(1 - \frac{37.5}{100} \right) = E_A \times 0.625 \\[5pt]\text{Efficiency of C is 60\% less than B:} \\E_C = E_B \times \left(1 - \frac{60}{100} \right) = E_B \times 0.4 \\\text{Substituting } E_B = E_A \times 0.625: \\E_C = E_A \times 0.625 \times 0.4 = E_A \times 0.25 \\[10pt]\textbf{Step 2: Work done by A and C in 42 days} \\[5pt]\text{Daily work of A and C } = E_A + E_C = E_A + 0.25E_A = 1.25E_A \\\text{Total work } = 42 \times 1.25E_A = 52.5E_A \\[10pt]\textbf{Step 3: Time taken by A, B, and C together} \\[5pt]\text{Combined efficiency: } E_A + E_B + E_C = E_A + 0.625E_A + 0.25E_A = 1.875E_A \\[5pt]\text{Time } = \frac{\text{Total work}}{\text{Combined efficiency}} = \frac{52.5E_A}{1.875E_A} = \frac{52.5}{1.875} = 28 \text{ days}$$​​