It takes 2 hours for Tanu and Deo to do a job. Tanu and Hari take 3 hours to do the same job. Deo and Hari take 6 hoursto do the same job. Which of the following statements is incorrect?

Correct option is D

Given:

• Tanu + Deo can complete the job in 2 hours → Work per hour = 1/2
• Tanu + Hari can complete the job in 3 hours → Work per hour = 1/3
• Deo + Hari can complete the job in 6 hours → Work per hour = 1/6

Let’s assign:

• T = Tanu's work per hour
• D = Deo's work per hour
• H = Hari's work per hour

Solution:

From the given:
T + D = 1/2 → (1)
T + H = 1/3 → (2)
D + H = 1/6 → (3)

Step 1: Add equations (2) and (3):
(T + H) + (D + H) = 1/3 + 1/6
→ T + D + 2H = 1/2

Now from equation (1):
T + D = 1/2

Substitute into the new equation:
1/2 + 2H = 1/2
→ 2H = 0
→ H = 0

So, Hari does no work at all

Now plug H = 0 into the other equations:
From (2): T + 0 = 1/3 → T = 1/3
From (1): T + D = 1/2 → 1/3 + D = 1/2 → D = 1/6

So:

• Tanu alone takes 1 ÷ (1/3) = 3 hours
• Deo alone takes 1 ÷ (1/6) = 6 hours
• Hari does no work

Check each option:

• A: Tanu alone can do the job in 3 hours → Correct
• B: Deo alone can do the job in 6 hours → Correct
• C: Hari does not work at all → Correct
• D: Hari is the fastest worker → Incorrect (He does no work)

Correct Option: (D) Hari is the fastest worker