Question

A person boarded a taxi that charges Rs 15 for the first km and Rs 8 for each additional km. He needs to pay Rs___ if he has to travel 16 km.

Answer 1

If we analyse the question carefully, we will know that the taxi fare for each km will form an arithmetic progression.
The first term is 15, which is the fare for the first km.
The common difference is 8, which is the fare for each additional km.
Now, the fare the person has to pay will be the fare for the first km and the fare for the remaining (n-1) additional km of distance travelled.
In this case, the distance he has to travel is 16 km, so for the first km, he must pay Rs 15, and for the rest 15 km, he must pay Rs 8 per km.
Now, a = 15, d = 8, and n = 16.
Therefore, the fare to be paid = nth term i.e. 16th term of the AP
$a_{16}=a+(n-1)d$
$a_{16}=15+(16-1)8$
$a_{16}=15+15\times 8$
$a_{16}=135$
Hence, the person must pay Rs 135.