Kanika was given her pocket money on 1st January, 2008. She puts Rs 1. On day1, Rs 2 on day2, Rs 3 on day3, and continued on doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and was found at the end of month she still has Rs 100 with her. How much money was her pocket money for the month?

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answer is A.

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Detailed Solution

Concept- The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number progression 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression that has a shared difference between two succeeding terms.
Consider that her pocket money is x rupees.
Sum of first `n' natural numbers is

Give her x rupees as pocket money.
She takes one rupee on the first day, two on the second, three on the third, and so on through the end of the month.
1 + 2 + 3 + ….. + 31
which comprise an AP with 31 terms, initial term (a) equal to 1, and common difference (d)=2-1=1
Sum of n terms