Correct Answer - Option 3 : 27 days
Given:
Ram can alone finish a work in 48 days.
The work is completed by Ram and Shyam in \(11\frac{1}{3}\)days.
Concept Used:
Total Work done = Time × Efficiency
Calculation:
Let the efficiency of Ram be x.
Let the efficiency of Shyam be y.
Ram can alone finish a work in 48 days.
The total work = 48 × x = 48x
The work is completed by Ram and Shyam in \(11\frac{1}{3}\)days.
That is the 6 days work done by Shyam and \(5\frac{1}{3}\) days work done by Ram.
The total work done = 6 × y + 16/3 × x
⇒ 48x = 6y + 16x/3
⇒ 128/3x = 6y
⇒ y = 64x/9
The time taken by Shyam to complete 4 times the work = 4 × 48x/y
⇒ 4 × 48x × 9/64x = 27 days
∴ The time taken by Shyam to complete 4 times the work is 27 days.