Solution:
Time taken by B to complete the work
$$\eqalign{ = 12 \times \frac{{100}}{{160}} \cr = \frac{{15}}{2}\,{\text{days}} \cr} $$
∴ (A + B)'s 1 day's work
$$\eqalign{ = \frac{1}{{12}} + \frac{2}{{15}} \cr = \frac{{5 + 8}}{{60}} \cr = \frac{{13}}{{60}} \cr} $$
Hence, the work will be completed in $$\frac{{60}}{{13}}$$ days

Solution:
(3m + 4w) × 7 = (2m + 1w) × 14
3m + 4w = 4m + 2w
m = 2w
m : w = 2 : 1
Total work = (3 × 2 + 4 × 1) × 7 = 70 unit
7w = 70 unit = $$\frac{{70}}{7}$$ = 10 days

Solution:
⇒ A can do $$\frac{1}{3}$$ of a work in 30 day
⇒ A completed work in 90 days
⇒ B can do $$\frac{2}{5}$$ of the same work in 24 days
⇒ B can completed work in 60 days
⇒ Let the total work = LCM (90, 60) = 180 unit
⇒ Efficiency of A = 3 unit/day
⇒ Efficiency of B = 2 unit/day
⇒ They both worked for 20 days, work done in 20 days = 20 × 5 = 100 unit
⇒ Remaining work = 180 - 100 = 80 unit
⇒ Remaining work done by C in 8 days
⇒ Efficiency of C = 10 unit/day
⇒ Efficiency of (A + B + C) = 15 unit/day
⇒ Work completed = $$\frac{{180}}{{15}}$$ = 12 days
∴ If all worked together, the work complete in 12 days.

Solution:
\[\begin{array}{*{20}{c}} {}{\text{A}}:{\text{B}} \\ {{\text{Efficiency}}}7:5 \end{array}\]
$$\eqalign{ {\text{A}} + {\text{B}} = 12 \times \frac{{35}}{2} = 35 \times 6{\text{ Total work}} \cr {\text{A}} = \frac{{35 \times 6 \times \frac{3}{5}}}{7} = 18{\text{ days}} \cr} $$

Solution:
A : B = 3 : 1
Total work = 4 × 18 = 72 unit
B = \[\frac{{72}}{1}\] = 72 days

Solution:
Let First division have x hectare of the land then second division will have (x - 12) hectare of land Now according to the question, 25 × (x - 12) = 21x + 300 or, x = 150 hectare Hence, the first division harvest 3150 tons tendu leaves.

Solution:
Since we know efficiency and time are inversely proportional to each other.

$$\eqalign{ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{P}}:{\text{Q}} \cr {\text{Efficiency }}3:4 \cr {\text{Time }}\,\,\,\,\,\,\,\,\,\,{\text{ }}4:3 \cr} $$