In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back up the next flag and continues the same way until all the flags are on the pole. The total distance covered is

740 m

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760 m

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820 m

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860 m

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Solution

The correct option is A
740 m

We have,
$d_{1}$ = distance travelled to pick up the first flag
= 10 + 10 = 2 $\times$ 10 = 20 m
$d_{2}$ = distance travelled to pick up the second flag
= 2 $\times$ (10 + 6) = 32m
$d_{3}$ = distance travelled to pick up the third flag
= 2 $\times$ (10 + 6 + 6)
= 44 m
$d_{10}$ = distance travelled to pick up 10th flag
= 2 $\times$ [10 + (10 - 1) $\times$ 6]m
$∴$ Total distance travelled
$= d_{1} + d_{2} + d_{3} + \dots + d_{10} = \frac{10}{2} [2 \times 20 + (10 - 1) 12] = 5 (40 + 108) = 5 \times 148$
= 740 m

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