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Q.

Kanika got her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continues 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?


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a

Rs. 700

b

Rs. 800

c

Rs. 900

d

Rs. 1000 

answer is B.

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Detailed Solution

Given, on Jan 1st, 2008 Kanika got her pocket money.
Let the monthly pocket money of Kanika be Rs. x.
The money which she deposited in a piggy bank and spent out of x is Rs. 204.
The money put in the piggy bank from Jan 1 to Jan 31 is represented as, 1+2+3+4+....+31.
From this we get a series, 1+2+3+4+....+31.
It can be observed that the values are, a=1, n=31, and the common difference d=1.
Substitute 1 for a and 1 for d and 31 for n in S n = n 2 2a+ n−1 d  to obtain  S 31   .
S 31 = 31 2 2 1 + 31−1 1 S 31 = 31 2 2+30 S 31 = 31 2 32  
S 31 =31 16 S 31 =496  
So, the money deposited in the piggy bank is Rs. 496.
The pocket money of Kanika for the month,
x−496−204=100 x−700=100 x=700+100 x=800  
Thus, the monthly pocket money of Kanika is Rs. 800.
Hence, the correct option is 2.
 
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