Ex 1: 10 men can lay a road 75 Km. long in 5 days. In how many days can 15 men lay a road 45 Km. long?

Solution:

Let x be number of days.

Ratio of days = 5 : x

Number of men is inversely proportional to number of days.

So inverse of ratio of men = 15 : 10 = 3 : 2

Length of road is directly proportional to number of days.

Therefore, ratio of lengths = 75 : 45 = 5 : 3

Now, 5 : x = 3 * 5 : 2 * 3

x * 3 * 5 = 5 * 2 * 3

x = (5*2*3)/(3*5)

x = 2

So, the number of days required = 2 days

Ex 2:  25 men can do a work in 27 hours then in how many hours 15 men can do the same work ?

Solution:

Since 25 men can do a work = 27 hours

So, 1 man can do a work = 27 * 25 hours

So, 15 men can do a work = (27 * 25)/15

                                          = (27 * 5)/3          {25 and 15 are divided by 5}

                                          = 9 * 5                  {27 and 3 are divided by 3}

                                          = 45 hours