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Raj alone can complete the work in 20 days and Radha alone can complete the work in M days while Ram alone can complete the work in 24 days. Raj and Radha can complete half of the work in 6 days. Radha works for 18 days then Raj and Ram join her to complete the remaining work. In what time total work gets completed?

Raj alone can complete the work in 20 days and Radha alone can complete the work in M days while Ram alone can complete the work in 24 days. Raj and Radha can complete half of the work in 6 days. Radha works for 18 days then Raj and Ram join her to complete the remaining work. In what time total work gets completed? Correct Answer <p style="">21.2 days</p>

Given:

Raj's 1 day's work = 1/20

Radha's 1 day's work = 1/M

Ram's 1 day’s work = 1/24

Calculation:

According to the question,

(1/20 + 1/M) = 1/12

⇒ 1/M = 1/12 – 1/20 = 1/30 = 1 day work of Radha

Total work done in 18 days by Radha = 18 × 1/30 = 3/5

(Raj + Radha + Ram)’s 1 days work = 1/20 + 1/30 + 1/24 = 1/8

⇒ Remaining work after 10 days = 1 – 3/5 = 2/5

Total time taken by all 3 to complete the remaining work = 2/5 × 8 = 3.2

∴ Total time required to complete the work = 18 + 3.2 = 21.2 days

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