Correct Answer - Option 3 : 9
Given:
Time taken by Ragini alone = 3 days more than both of them worked together
Time taken by Raghav alone = 12 days more than both of them worked together
Calculation:
Let the time both of them took to make the carpet be x.
Time taken by Ragini alone = x + 3
Time taken by Raghav alone = x + 12
∴ one day of work when they both work together = Sum of their individual per day work
⇒ 1/x = 1/(x + 12) + 1/(x + 3)
⇒ 1/x = (2x + 15)/(x2 + 15x + 36)
⇒ x2 + 15x + 36 = 2x2 + 15x
⇒ x = 6
∴ time taken by Ragini alone = 6 + 3
⇒ 9 days
Ragini alone make the carpet in 9 days.