[50] A contractor undertook to make 15 km of roadway in 40 weeks. In 10 weeks, 3 km was complete by 180 m

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A contractor undertook to make 15 km of roadway in 40 weeks. In 10 weeks, 3 km was complete by 180 men working 8 hours a day. The men then agreed to work 1 hour a day overtime, And some boys were engaged to assist them, the work was finished in the stipulated time(40 weeks). How many boys were employed, if the work of 3 boys is equal to that of 2 men?

Explanation:

Let the capacity of man = 3 units, and boy = 2 units per hour.

Now total work = 3 × 180 × 8 × 7 × 10 = 3 km. - - - - - - - (1)

Let k boys were recruited. Now total work = (3 × 180 + 2 × k) × 9 × 7 × 30 = 12km. - - - - - - (2)

By dividing 2nd equation by 1st,

=> (540+2k) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4(540+2k) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4

=> k = 50.

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