A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month
A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month. How much did he save in the first month?
Let the money saved by the man in the first month be ₹a.
It is given that in each month after the first, he saved ₹100 more than he did in the preceding month. So, the money saved by the man every month is in AP with common difference ₹100.
∴ d = ₹100
Number of months, n = 10
Sum of money saved in 10 months, S10 = ₹33,000
Using the formula, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$, we get
$S_{10}=\frac{10}{2}[2 a+(10-1) \times 100]=33000$
$\Rightarrow 5(2 a+900)=33000$
$\Rightarrow 2 a+900=6600$
$\Rightarrow 2 a=6600-900=5700$
$\Rightarrow a=2850$
Hence, the money saved by the man in the first month is ₹2,850.
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