To do a certain work, A is 40% more efficient than B. Working together, they can do the same work in 15 days. A started the work and left after 15 days. B and C together completed the remaining work in next 10 days. C alone can do one-third of the original work in:

Let the efficiency of B be 10.
Since A is 40% more efficient than B, efficiency of A = 10×1.4=14.
Combined efficiency of A and B = 14+10=24.

Working together, they complete the work in 15 days.

Total Work=Combined Efficiency×Days=24×15=360 units
A started the work and worked for 15 days:

Work done by A=14×15=210 units
Remaining Work=360−210=150 units
B and C together completed the remaining 150 units in 10 days:

Combined efficiency of B and C=
10
150
​
=15
Since efficiency of B = 10, efficiency of C = 15−10=5.

We need to find the time taken by C alone to do one-third of the original work:

One-third of total work=
3
360
​
=120 units
Time taken by C=
Efficiency of C
120
​
=
5
120
​
=24 days