A is 25% more efficient then B. A works for ‘D’ days and completed 1/3 of work and left the work and remaining work is completed by B in ‘D…

A works for D days and completed 1/3rd of work

Work done by A in D days = 1/3

A alone can complete the work = 3D days

Work done by A in 1 day = (1/3) × (1/D) = 1/3D

Ratio of time taken by A and B = 100 : 125

Let’s assume B alone can complete the work in in x days.

⇒ 100 / 125 = 3D/x

⇒ x = 15D/4

Remaining work = 1 - 1/3 = 2/3

2/3rd of work completed by B in (D + 12) days.

⇒ 2/3 = (4/15D) × (D + 12)

⇒ 30D = 12D + 144

⇒ 18D = 144

⇒ D = 8

A can alone complete the work in 8 × 3 = 24 days

B alone can complete the work in = 15/4 × 8 = 30

If A and B work together, work will be completed in = 1/[(1/24) + (1/30)] = 1/(9/120) = 120/9

∴ A and B together complete the work in 120/9 = $(13\frac{1}{3})$ Days