| If 17 labourers can dig a ditch 26 m long in 18 days, working 8 h a day, then how many more labourers should be engaged to dig a similar ditch 39 m long in 6 days, each labourer working 9 h a day? |
A) 34
B) 51
C) 68
D) 85
Correct Answer: B
Solution :
| 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] |
| \[\left. \begin{matrix} \text{Length} & \text{26}\,\,\text{:}\,\,\text{39} \\ \text{Days} & \text{6}\,\,\text{:}\,\,\text{18} \\ \text{Hours}\,\text{per}\,\text{day} & \text{9}\,\,\text{:}\,\,\text{8} \\ \end{matrix} \right\}\text{::}\,\,\text{17}\,\,\text{:}\,\,x\] |
| \[\therefore \] \[(26\times 6\times 9\times x)=(39\times 18\times 8\times 17)\] |
| \[\Rightarrow \] \[x=\,\,\frac{(39\times 18\times 8\times 17)}{(26\times 6\times 9)}=68\] |
| \[\therefore \] Number of more labourers \[=(68-17)=51\] |
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