Kanika was given her pocket money on Jan 1^{t | vedclass

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(C) Let her pocket money be $Rs.\, x$.She puts money into her piggy bank following the pattern: $1, 2, 3, \dots, 31$ (since January has $31$ days).Thi

Vedclass · Accepted Answer

$800$

Vedclass · Answer

(C) Let her pocket money be $Rs.\, x$.She puts money into her piggy bank following the pattern: $1, 2, 3, \dots, 31$ (since January has $31$ days).This forms an Arithmetic Progression $(AP)$ where the first term $a = 1$,the common difference $d = 1$,and the number of terms $n = 31$.The sum of the first $n$ terms is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$.$S_{31} = \frac{31}{2}[2(1) + (31 - 1)(1)] = \frac{31}{2}[2 + 30] = \frac{31 	imes 32}{2} = 31 	imes 16 = 496$.So,she put $Rs.\, 496$ into her piggy bank.She also spent $Rs.\, 204$ and had $Rs.\, 100$ left.The total pocket money $x$ is the sum of the money put in the piggy bank,the money spent,and the money remaining:$x = 496 + 204 + 100 = 800$.Therefore,her pocket money for the month was $Rs.\, 800$.

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