Question

Ravi takes thrice the time of manish to complete a piece of work, and manish takes five times of pawan to complete the same work. if they work together then they can finish the work in 30 days. then find the time taken by them to complete the work individually?

Answer 1

Given :-

• Ravi takes = 3 * Time taken by manish .
• Manish takes = 5 * Time taken by pawan .
• Together they can finish the work in = 30 days.

To Find :-

• find the time taken by them to complete the work individually ?

Solution :-

given that,

→ Manish takes = 5 * Time taken by pawan .

so,

→ Manish time : Pawan time = 5 : 1 .

also, given,

→ Ravi takes = 3 * Time taken by manish .

so,

→ Ravi time : Manish time = 3 : 1 .

then,

→ Ravi time : Manish time : Pawan time = 15 : 5 : 1 .

we know that,

• Time ∝ 1/Efficiency .

therefore,

→ Ravi Efficiency : Manish Efficiency : Pawan Efficiency = (1/15) : (1/5) : (1/1) = (1 : 3 : 15)/15 = 1 : 3 : 15 .

hence,

→ Total work = (Efficiency of all three) * Time taken by all of them = (1 + 3 + 15) * 30 = 19 * 30 = 570 units .

∴

• Time taken by Ravi alone to complete the work = (Total work) / Efficiency = 570/1 = 570 Days.
• Time taken by Manish alone to complete the work = (Total work) / Efficiency = 570/3 = 190 Days.
• Time taken by Pawan alone to complete the work = (Total work) / Efficiency = 570/15 = 38 Days.

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