Question

In a potato race 20 potatoes are placed in a line at intervals of 4 metres with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

Answer 1

We have the following diagram:

Starting point = S

Distance travelled to bring the first potato = 24 + 24 = 48 m

Distance travelled to bring the second potato = 2(24 + 4) = 56 m

Distance travelled to bring the third potato = 2(24 + 4 + 4) = 64 m

Therefore, the series will be = 48, 56, 64, …

Which an A.P. in which a = 48, d = 56 – 48 = 8

We have to find the total distance to bring all the potatoes back

So, n = 20

∴ Sn = `n/2[2a + (n - 1)d]`

⇒ S₂₀ = `20/2 [2 xx 48 + (20 - 1)8]`

= 10[96 + 152]

= `10 xx 248`

= 2480 m

Hence, the required distance = 2480 m.