If 15 men can dig a trench 35 m long in 1 day, then how many men can dig a similar trench 84 m long in 1 day ?

Given:

Men required for 35 m trench = 15 men

Men required for 84 m trench = ?

Let men required for 84 m trench = x men

Length of trench : Number of men

35 : 84 :: 15 : x

By the rule: Product of Extremes = Product of Means:

35 × x = 84 × 15

x = $\dfrac{84 \times 15}{35}$

x = $\dfrac{84 \times 3}{7}$

x = 12 x 3

x = 36

Hence, 36 men are required to dig the 84 m trench.