Anita and Anand can complete a work in 12 days and 18 days respectively. They undertook to complete that work for ₹48,000. With the help of Arun, they completed the work in 6 days. Find the sum of the shares of Anita and Anand (in ₹).

Let the total work be the LCM of individual days (12,18,6) = 36 units.
Now, let's find their individual efficiencies (work done per day):

Efficiency of Anita (E
Anita
​
) =
12
36
​
=3 units/day

Efficiency of Anand (E
Anand
​
) =
18
36
​
=2 units/day

When Anita, Anand, and Arun work together, they complete the work in 6 days.

Combined Efficiency (E
Anita
​
+E
Anand
​
+E
Arun
​
) =
6
36
​
=6 units/day

Now, find the efficiency of Arun:

3+2+E
Arun
​
=6⟹E
Arun
​
=1 unit/day
Wages are distributed in proportion to the total work done or efficiency since they work together for the same amount of time:

Ratio of shares=E
Anita
​
:E
Anand
​
:E
Arun
​
=3:2:1
Total ratio parts = 3+2+1=6 parts
Total amount = ₹48,000

We need to find the sum of the shares of Anita and Anand:

Combined share fraction=
6
3+2
​
=
6
5
​

Combined share value=
6
5
​
×48000=5×8000=₹40,000