Kiran can do a certain piece of work in 15 days. Kiran and Garima can together do the same work in 10 days, and Kiran, Garima and Mehak can do the same work together in 9 days. In how many days can Kiran and Mehak do the same work?

Given:

Kiran can do the work in 15 days.

Kiran and Garima can do the work together in 10 days.

Kiran, Garima, and Mehak can do the work together in 9 days.

Formula used:

Work efficiency = 1/Time taken

Total work = LCM of individual times

Combined efficiency = Sum of individual efficiencies

Calculation:

Let the total work be LCM(15, 10, 9) = 90 units.

Efficiency of Kiran = \(\dfrac{90}{15} = 6 \, \text{units/day}\)

Efficiency of Kiran and Garima = \(\dfrac{90}{10} = 9 \, \text{units/day}\)

⇒ Efficiency of Garima = 9 - 6 = 3 units/day

Efficiency of Kiran, Garima, and Mehak = \(\dfrac{90}{9} = 10 \, \text{units/day}\)

⇒ Efficiency of Mehak = 10 - (6 + 3) = 1 unit/day

Efficiency of Kiran and Mehak = 6 + 1 = 7 units/day

Time taken by Kiran and Mehak = \(\dfrac{\text{Total work}}{\text{Efficiency}}\)

⇒ Time = \(\dfrac{90}{7}\) days

⇒ Time = \(\dfrac{90}{7}\) days

∴ The correct answer is option (4).