Question

Question 34
Kanika was given her pocket money on Jan $1^{st}$, 2008. She puts Rs.1 on day 1, Rs.2 on day 2, Rs.3 on day 3 and continued 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 found that at the end of the month she still had Rs.100 with her. How much was her pocket money for the month?

Answer 1

Let her pocket money be Rs. x.
From this money, she takes Rs.1 on day 1, Rs. 2 on day 2, Rs.3 on day 3 and so on until the end of the month.
1 + 2 + 3 + 4 + ….. + 31
Which form an AP in which, number of terms is 31, first term (a) = 1 and common difference (d) = 2 – 1 = 1
Sum of n terms $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$S_{31}=\frac{31}{2}[2\times 1+(31-1)\times 1]$
$=\frac{31}{2}(2+30)=\frac{31\times 32}{2}$
$=31\times 16=496$
So, Kanika takes Rs. 496 till the end of the month from x.
Also, she spent Rs. 204 of her pocket money and found that at the end of the month she still has Rs. 100 with her.
Now, according the condition,
(x - 496) - 204 = 100
$\Rightarrow$ x - 700 = 100
$\therefore$ x = Rs. 800
Hence, Rs. 800 was her pocket money for the month.