Chain Rule Q32

32. If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours a day; how many more labourers should be engaged to dig a similar ditch 39 m long in 6 days, ech labourer working 9 hours a day?

[A] 34

[C] 68

[B] 51

[D] 85

Answer : B

Explanation :

Let the total number of men to be engaged be x.

More length, More labourers (Direct Proportion)

Less days, More labourers (Indirect Proportion)

More hours per day, Less labourers (Indirect Proportion)

Length 26 : 39 Days 6 : 18 Hours per day 9 : 8  :: 17  : x

(26 x 6 x 9 x x) = (39 x 18 x 8 x 17)

x = (39 x 18 x 8 x 17) (26 x 6 x 9)  = 68

Number of more labourers = (68 - 17) = 51