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A and B can do a work in 60 days and 75 days respectively. Both A and B work together for 10 days. After that B leaves the work but A continues. then after 6 days, C also joins. Then after 24 days, work is completed. How much time it will take C alone to the complete their work?
1. 130 days
2. 120 days
3. 122 days
4. 125 days
5. 121 days

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Correct Answer - Option 2 : 120 days

Given:

A and B can do a work in 60 days and 75 days respectively

Both A and B work together for 10 days. 

Calculation:

Work done by A in 1 day = 1/60

Work done by B in 1 day = 1/75

Work done by both (A + B) in 1 day = (1/60 + 1/75)

⇒ (5 + 4)/300

⇒ 9/300 = 3/100

Now, Work done by both (A + B) in 10 days = [10 × (3/100)] = 3/10

Remaining work = [1 – (3/10)] = 7/10

Work done by A in 6 day = [6 × (1/60)] = 1/10

Now, Remaining work = (7/10 – 1/10) 

⇒ (7 – 1)/10 = (6/10) days

According to the question:

(A + C) × 6/10 = 24

⇒ (A + C) = (24 × 10)/6 = 40 days

Work done by both (A + C) in 1 days = 1/40

Work done by C in 1 day = (1/40 – 1/60) 

⇒ (3 – 2)/120 = 1/120

∴ Total time work done by c  in 120 days.

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