Inverse relation of efficiency and time: Ajit is 3 times as efficient as Bablu. What is the ratio of the number of days required by Ajit and Bablu, respectively, to finish the job working alone?

Introduction / Context:
This tests the inverse relationship between efficiency and time. If Ajit is faster (more efficient), he takes fewer days. The product (efficiency * time) needed for one job is constant (equal to 1 job).

Given Data / Assumptions:

• Efficiency_Ajit = 3 * Efficiency_Bablu.
• Each works alone at a constant rate.

Concept / Approach:
Let Bablu’s time be T. Since Ajit is 3 times as efficient, Ajit’s time is T/3. Therefore, (Ajit days) : (Bablu days) = (T/3) : T = 1 : 3.

Step-by-Step Solution:
If rate_B = r, then rate_A = 3r.Time_B = 1/r, Time_A = 1/(3r) = (1/3)*(1/r).Thus, Time_A : Time_B = 1/3 : 1 = 1 : 3.

Verification / Alternative check:
Pick numbers: if Bablu needs 30 days, Ajit needs 10 days → 10:30 = 1:3, matching the reasoning.

Why Other Options Are Wrong:

• 3:1 and 6:3 invert the inverse relationship; those are efficiency ratios, not time ratios.
• 3:6 simplifies to 1:2, still incorrect.

Common Pitfalls:

• Confusing efficiency ratio with time ratio. They are reciprocals.

Final Answer:
1 : 3