Chain Rule - Study Mode

[#66] If 17 labourers can dig a ditch 26 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, each labourer working 9 hours a day ?
Correct Answer

(B) 51

Explanation

Solution: Let the total number of men to be engaged be $$x$$ More length, More labourers (Direct proportion) Less days, More labourers (Indirect proportion) [left. x08egin{gathered}
,,,,,,,,,,,,{ ext{Lentgh 26}}:39 hfill \
,,,,,,,,,,,,,,,,,,,{ ext{Days 6}}:18 hfill \
{ ext{Hours per day }}9:8 hfill \
end{gathered}
ight}::17:x] $$eqalign{
& herefore { ext{ }}26 imes 6 imes 9 imes x = 39 imes 18 imes 8 imes 17 cr
& Leftrightarrow x = frac{{left( {39 imes 18 imes 8 imes 17}
ight)}}{{left( {26 imes 6 imes 9}
ight)}} cr
& Leftrightarrow x = 68 cr} $$ ∴ Number of more labourers = (68 -17) = 51