[325 m] Two boys A and B run at 4 1⁄5 and 8 km an hour respectively. A having 150 m start and the course bei

For Competitive Exams

Two boys A and B run at 4 1⁄5 and 8 km an hour respectively. A having 150 m start and the course being 1 km, B wins by a distance of

325 m

60 m

120 m

275 m

Explanation:

A has a start of 150 m. So A has to run 1000-150=850 metre while B has to run 1000 metre.

$\text{Speed of A = }4 \dfrac{1}{5}\text{ km/hr }= \dfrac{21}{5}\text{ km/hr }= \dfrac{21}{5} × \dfrac{5}{18} = \dfrac{21}{18} = \dfrac{7}{6}\text{ m/s}$

$\text{Speed of B = 8 km/hour = }8 × \dfrac{5}{18} = \dfrac{20}{9}\text{ m/s}$

$\text{Time taken by B to travel 1000 metre = }\dfrac{\text{distance}}{\text{Speed of B}} = \dfrac{1000}{\left(\dfrac{20}{9}\right)}= \text{ 450 second}$

$\text{Distance travelled by A by this time = time × speed of A = }450 \times \dfrac{7}{6}= 525\text{ metre}$

Hence, A win by $\left(850-525\right)$=325 metre

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