Question

A driver was collecting water sample from a lake.He collected a sample at every interval of 3m,starting at 5m below the water surface. The final sample was collected at a depth of 35m.How many sample did he collect.

Answer 1

first he take sample from 5m below
at last from 35m depth
so total distance of tested= 35-5 = 30
at every 3m he took sample
so no. of times he collect sample= 30/3+1 = 10
because for 5th metre we have take one sample and starts taking the sample

Answer 2

The easiest method would be using A.P (hope you have learnt it )

Represent the given data in series like given below:

A.P: 5,8,11..........,35


According to the A.P formula we have;

＜ an= a+ (n-1)d ＞


Here,
a=5 (distance at which first sample is collected/the first term)

an= 35 (distance at which last sample is collected/last term)

d= secound term - first term
=8-5=3 (interval at which sample is collected)

n= no of samples collected,which is what we need to find
Substitute all the values in the formula

We get,
an=a+(n-1) × d

35=5+(n-1) × 3
30=(n-1)×3
30=3n-3
33=3n
11=n
Which is the required number of samples collected.
Hence at the end of 35m 11 samples will be collected.