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An engineer undertakes a project to build a road 15 km long in 300 days and employs 45 men for the purpose. After 100 days, he finds 2.5 km of the road has been completed. Find the (approx.) number of extra men he must employ to finish the work in time.
Answer & Solution
Correct Answer:
Option
D
Variation Method:
In 100 days only 2.5 km road i.e. 16.66 % of work has been completed
Arrows show the directions of variation of quantity with respect to each other $$\frac{{\text{x}}}{{45}} = \frac{{100 \times 12.5}}{{200 \times 2.5}}$$ x = 113 men; Required men to be increased, = 113 - 45
= 68
| Men | Days | Road (km) |
| 45 | 100↓ | 2.5 |
| x↑ | 200 | 12.5↑ |
Arrows show the directions of variation of quantity with respect to each other $$\frac{{\text{x}}}{{45}} = \frac{{100 \times 12.5}}{{200 \times 2.5}}$$ x = 113 men; Required men to be increased, = 113 - 45
= 68
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Login4500 man days / 2.5 km = 1800 man days per km
12.5 km to build * 1800 man days per km = 22,500 man days to complete the road
22,500 man days / 200 days = 67.5 men, rounding to 68 men working 200 days to complete the road
Why wouldn't the number of extra men be 68 - 45 = 23?