Question

Given: Anuj takes 1 day to complete a job. Bharat takes twice the time as Anuj to complete the same job. Chetan takes twice the time as Bharat to complete that job. Dhiraj takes twice the time as Chetan to complete that job.
(A) Chetan and Dhiraj will take 8/3 days to complete the work
(B) The second fastest pair to complete the work is Anuj and Dhiraj
(C) The second slowest pair to complete the work is Bharat and Dhiraj 
(D) Bharat and Dhiraj will take 4/3 days to complete the work 
Choose the correct answer from the options given below:

• A. (A), (B) and (C) only
• B. (A) and (D) only
• C. (A) and (C) only
• D. (A) only

Answer 1

The Correct Option is C

To determine the correct answer, let's analyze each given option based on the work rates of Anuj, Bharat, Chetan, and Dhiraj.

1. Anuj completes the job in 1 day. His work rate is \(\frac{1}{1} = 1\text{ job/day}\). 
2. Bharat takes twice the time of Anuj, so he takes 2 days to complete the job. His work rate is \(\frac{1}{2} \text{ job/day}\).
3. Chetan takes twice the time of Bharat, so he takes 4 days. His work rate is \(\frac{1}{4} \text{ job/day}\).
4. Dhiraj takes twice the time of Chetan, so he takes 8 days. His work rate is \(\frac{1}{8} \text{ job/day}\).

Next, let's evaluate the given statements:

• (A) Chetan and Dhiraj will take 8/3 days to complete the work.
  • The combined work rate of Chetan and Dhiraj is \(\frac{1}{4} + \frac{1}{8} = \frac{3}{8} \text{ jobs/day}\).
  • The time taken to complete one job at this rate is \(\frac{1}{\frac{3}{8}} = \frac{8}{3} \text{ days}\).
  • This statement is correct.
• (B) The second fastest pair to complete the work is Anuj and Dhiraj.
  • Pairs considered: Anuj & Bharat, Anuj & Chetan, Anuj & Dhiraj, Bharat & Chetan, Bharat & Dhiraj, Chetan & Dhiraj.
  • The pair Anuj & Bharat has the highest rate after Anuj & Chetan, thus faster than Anuj & Dhiraj.
  • This statement is incorrect.
• (C) The second slowest pair to complete the work is Bharat and Dhiraj.
  • The combined work rate for Bharat & Dhiraj is \(\frac{1}{2} + \frac{1}{8} = \frac{5}{8} \text{ jobs/day}\).
  • Calculate work rate for other pairs and compare:
    • Anuj & Dhiraj: \(\frac{1}{1} + \frac{1}{8} = \frac{9}{8} \text{ jobs/day}\)
    • Chetan & Dhiraj: \(\frac{3}{8} \text{ jobs/day}\)
  • Bharat & Dhiraj is indeed the second slowest pair after Chetan & Dhiraj.
  • This statement is correct.
• (D) Bharat and Dhiraj will take 4/3 days to complete the work.
  • The combined work rate of Bharat and Dhiraj is \(\frac{5}{8}\) jobs/day.
  • The time taken to complete one job is \(\frac{1}{\frac{5}{8}} = \frac{8}{5} \text{ days}\).
  • This statement is incorrect.

Based on our analysis, the correct answer is: (A) and (C) only.