A man saves Rs 32 during the first year.
Question:

A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.

Solution:

Let n be the time in which the man saved Rs 200.

Here, d= 4, a = 32

We know:

$S_{n}=\frac{n}{2}\{2 a+(n-1) d\}$

$\Rightarrow 200=\frac{n}{2}\{2 \times 32+(n-1) 4\}$

$\Rightarrow 400=64 n+4 n^{2}-4 n$

$\Rightarrow 4 n^{2}+60 n-400=0$

$\Rightarrow n^{2}+15 n-100=0$

$\Rightarrow n^{2}+20 n-5 n-100=0$

$\Rightarrow(n+20)(n-5)=0$

$\Rightarrow n=5, n=-20 \quad$ (Rejecting the negative value)

Therefore, the man took 5 years to save Rs 200.

 

 

 

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