Question

Kanika was given her pocket money on 1st January 2008 .she puts ₹1 on day 1, ₹2 on day 2,₹3on day 3 and continued doing so till the end of the month, from this money into the piggy bank. she also spent ₹204 of her pocket money and found that at the end of the month she still had ₹100 with her.how much was her pocket money for the month?​

Answer 1

†Question:

• Kanika was given her pocket money on Jan 1st, 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?

†Solution:

• ${\bf{Let\: her\: pocket\: money\: be\: Rs \:x}}$

Now, she takes Rs 1 on day 1, Rs 2 on day 2, Rs 3 on day 3 and so on till the end of the month, from this money.

• This makes a list1, 2, 3, - - - , 31 [ as Jan has 31 days]
• Clearly this is an AP with first term, a = 1 and d = 1 and no of terms = 31

→So amount of money she puts in piggy bank in a month

Sum of n terms of this AP,

Sn = n/2[2a+(n-1)d]

=31/2 [2×1+(31-1)1]

=31/2[2+30]

= 31/2×32

=31×16 =496

→So, Kanika puts Rs 496 till the end of the month from her pocket money

Also, she spent 204 of her pocket money and found that at the end of the month, she still has Rs 100 with her.

Now, according to the condition,

x - 496 - 204 = 100

x - 700 = 100

x = 800

${\bf{\green{So \:she \:gets \:800\: Rs\:as\: her\: pocket\: money}}}$

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